The Catholic faithful have much to do in the wake of the visit to America by Pope Benedict XVI, who encouraged hopefulness but also challenged his flock to take up the work of healing a church battered by the fallout from the clergy sex abuse scandal, the dearth of men and women becoming priests and nuns, and the loss of parishes and parochial schools as church membership contracts.

The tasks he set out for Catholic followers on his first visit to America in his new role as the bishop of Rome are not small ones — again and again, he made it clear that he thinks the hope that headlined his trip would be contingent on the Catholic faithful laying the groundwork for the American church’s future vibrancy and viability.

“Today’s celebration is more than an occasion of gratitude for graces received,” he said yesterday during his final public appearance before leaving for home last night, a Mass celebrated at Yankee Stadium. “It is also a summons to move forward with firm resolve to use wisely the blessings of freedom, in order to build a future of hope for coming generations.”

To the surprise of many, he repeatedly expressed shame for the clergy sexual abuse scandal throughout the trip, but he coupled his concern and sympathy with calls for both the laity and the clergy to forgive and to come together to heal the deep wounds that divide the church.

The only way to move forward, he suggested, is “in hope, in love for the truth and for one another.”

He addressed a beleaguered group of Catholic educators, some of whom have been holding bitter debates about the role of Catholic culture in Catholic universities and colleges, while others are dealing with declining enrollments that could lead to the disappearance of inner-city parochial schools in the next decade.

The solution to their problems, he suggested, is to embrace the Catholic-ness of Catholic schools and re-focus their missions on teaching religious truth. The suggestion could be a challenge for many colleges that have adopted more liberal policies, such as welcoming graduation speakers that back abortion rights and allowing gay and lesbian student groups, and for parochial schools that increasingly depend on non-Catholic students to stay open.

Addressing worries that the church is losing out to the temptations of secular society, he called on Catholics to renew their faith, to unite under a core set of religious principles, and to embrace the new immigrants that lately have become the main source of church growth. In other words, Benedict suggested it is up to the faithful to prevent the American Catholic Church from going the way of more religiously indifferent Western Europe.

Yet, for all that he urged Catholics to take on the task of healing their church, the enthusiasm inspired by Benedict’s presence — he was compared throughout the week to a rock star, as breathless crowds greeted him with the same screaming exuberance teenage fans showed for the Beatles — is likely to help give the church the boost it needs to weather its troubles in the near future.

The rock star analogy seemed most apt at a rowdy rally in Yonkers Saturday, where 25,000 young people danced, cheered, sang, and listened with rapt attention to the pope as he recalled growing up in Nazi Germany and called on them to reject relativism and cling to truth.

Yesterday, tens of thousands from across the city and the country flooded into Yankee Stadium for a more formal afternoon Mass, and thousands more filled the blocks nearby, dancing, singing, and praying that the pope’s blessings would filter beyond the stadium walls.

In line to enter the stadium, Sister Geraldine Cregg, a 70-year-old nun from one of the region’s largest orders, St. Joseph in Brentwood, said she hoped the pope’s presence would inspire more women to become nuns. Her order has dropped to 700 from 3,000 nuns when she joined 49 years ago, and only one woman is planning to join this year.

An immigrant from Haiti who won the lottery for Mass tickets in her Brooklyn parish, Claire Guerrier, said she hoped the pope’s United Nations speech about human rights would persuade the world to take an interest in the hunger tearing apart her home country.

Lawrence Fejokwu, 33, of Niger, and Ifeoma Ikeagu, 26, of Queens, said they hoped the pope’s trip would leave a lasting impression on young people and draw more to join the church.

Maria Gonzalez, 30, an immigrant from Mexico who waited for hours outside of the stadium with her husband and five children, ages 1 to 9, said she hoped their proximity to the pope might produce a miracle and cure the malignant tumor in her belly.

“Besides a miracle, we just want to see him,” her husband, Francisco Jimenez, 29.

Benedict didn’t promise miracles while he was here, instead focusing on the courage his followers would need going forward to follow his prescriptions for saving their church. Faith, he said, “means not losing heart in the face of resistance, adversity, and scandal.”

One of the key tests of the success of the journey will be whether the Catholic Church begins to overcome the challenge of secularism and the appeal of Pentecostalism, or whether more Catholics will continue to drift away.

The director of the Trinity College Institute for the Study of Secularism in Society and Culture, Barry Kosmin, said that unlike his predecessor, Pope John Paul II, who was concerned about converting nonbelievers, Benedict’s primary concern is believers who have become indifferent or ambivalent about the Church.

“He’s not worried about people who don’t believe, he’s worried about people who don’t care very much,” Mr. Kosmin said.

Whether a younger generation of Catholics — the “Facebook kids,” as Mr. Kosmin called them — is inspired by the visit to turn away from their computers to sit down and read one of the pope’s encyclicals, or to just begin attending church more often, is to be seen.

“There’s definitely a kind of magic, but does that play today? I don’t know,” Mr. Kosmin said. “Maybe his presence will make a big difference.”

The outcome of past papal visits suggest that the Catholic Church, particularly in Washington, D.C., where he spent part of his visit, and in New York, can expect an initial boost in church attendance and recruitment of priests and nuns. Two years after John Paul visited Denver in 1993 for an international youth conference, church attendance there jumped by more than 7% after declining 11% in the four years before the visit. Also, parochial school enrollment increased by 11%, a record number of adults joined the church, and the number of women expressing interest in becoming nuns spiked.

The attention surrounding Benedict’s visit, with news cameras following his every move throughout the week and eagerly cataloguing a number of firsts, including the first papal visit to an American synagogue, the first to St. Patrick’s Cathedral, and the first to the pit of ground zero — where he prayed alongside public officials and families of victims of the September 11, 2001, terrorist attacks — ensured that the pope’s words were spread far and wide. The president of the Catholic Education Institute at Marist College, the Reverend John Piderit, called this weekend’s visit exciting, and a “great shot in the arm” particularly for priests and nuns. But he said the impact would depend on how American Catholics act on the pope’s words of encouragement.

“That enthusiasm is great, but that fades away. It’s going to make a difference because we discuss the ideas that he talked about,” he said. “I think that it has to be a serious discussion which ensues.” The most serious topic to be taken up will be the clergy sexual abuse scandal, which became a central focus of Benedict’s trip. His efforts to address it openly — especially his unprecedented meeting with a group of victims — appeared to create new possibilities to resolve the anger and frustration among many Catholics over how the church hierarchy has handled the issue.

“We are amazed. We are stunned,” Anne Wilson, one of the New York City chapter leaders of Voice of the Faithful, a group formed in the wake of the clergy abuse, said.

“I see it as seismic. I think it will be different,” she added during an interview at her Brooklyn Heights home over the weekend.

Before Benedict’s visit, Mrs. Wilson and her husband, Ed, said their organization had considered publishing an open letter to the pope calling for changes in how the church has handled the issue, but it instead published an advertisement calling on the Catholic faithful to join in the cause because it assumed the pope wouldn’t be listening. Now, that has changed, Mrs. Wilson said.

Although members of groups such as the Voice of the Faithful continued to call on the pope to follow up on his words with actions such as removing some bishops who they say mishandled the abuse, Mrs. Wilson said she believed Voice of the Faithful would now be working on a new letter — this one addressed to the pope — to discuss the next steps.

More importantly, they said the pope’s focus on the issue has given the laity new leverage to take up the issue with the church leadership in America. Groups such as Voice of the Faithful have lobbied for stronger role for the laity in decision-making in the church in general, especially as lay leaders have taken on more responsibilities in churches as the number of priests and nuns has decreased. “There’s a signal going out to the bishops to get on board with this,” Mr. Wilson said. “We’re encouraged.”

Some were less impressed. Daniel Maguire, a moral theology professor at Marquette University in Wisconsin, a Catholic institution, said he was disappointed that the pope had reiterated his position that Catholic educators should adhere to Vatican theology, which sits to the right of some Catholic academics in America, and that he didn’t address the problems of global warming or the Iraq war.

“The rigidity at the top is actually driving people away and it will continue to do that,” he said.

The top could see some major changes, however — in New York, anyway. Benedict’s visit has prompted some speculation that Edward Cardinal Egan of the Archdiocese of New York will be on his way out soon. He has presided over the archdiocese for the past year after handing in his resignation, with some suggesting a decision about who would take over was on hold as the city prepared for the archdiocese’s bicentennial celebration and the papal visit.

Now, it’s likely the cardinal, who has been criticized by some progressive groups for his secrecy about finances and the sexual abuse scandal, will be replaced shortly.

Despite the focus Benedict’s trip brought to the church’s weaknesses and challenges, the visit seemed to serve its main purpose of rejuvenating millions of the faithful, even some who have been weighed down by pessimism.

The pastor of St. Joseph’s parish on the Upper East Side, Monsignor John Sullivan, who hosted the pope’s meeting with ecumenical leaders, ticked off a list of problems facing the Church as he waited for the pope to arrive on Friday.

His former parish in the Bronx was merged, or “submerged,” as he likes to say, because of dwindling membership. “They sunk it,” he added. The enrollment at St. Joseph’s school and church attendance also is down, although he says it is staying afloat for now. He has also been upset about how the priest abuse scandal has been handled, and is saddened by the lack of recruits for the priesthood.

Asked about whether the pope’s visit might help, he smiled: “Of course it’s wonderful,” and anyway, he added, “the church has worked out of every difficulty for 2,000 years now.”