Coaches are never satisfied. Neither are players, at least the great ones . That’s why New York Knicks Coach Tom Thibodeau isn’t ready to toss bouquets at his team for clinching no worse than a fourth seed and home-court advantage in the first round of the Eastern Conference playoffs.

“You want to get better,” Mr. Thibodeau said recently.

A 111-107 victory over the Brooklyn Nets on Friday night at Madison Square Garden means the Knicks (49-32) can earn the third seed with a victory in their regular-season finale Sunday against the Chicago Bulls. New York can move up to the second seed  with a win and a loss by the Milwaukee Bucks.

Regardless of their playoff position, Mr. Thibodeau said the Knicks aren’t quite playoff-ready. “To me, there’s a lot of things we have to get better at to prepare ourselves for the end,” he said, adding, “There’s still a lot of things we have to work on.”

The Knicks’ All-Star guard, Jalen Brunson, who scored 30 points against the Nets, echoed the coach’s sentiments. “We’ve been talking about not jogging toward the finish line, but sprinting through it,” he said, “and making sure we’re playing as hard as we can to get better every day and not just easing toward the end.”

In truth, the Knicks are finishing about as well as could be expected. After a recent stretch where they lost four of five games, they have won four straight heading into Sunday’s regular-season finale at Madison Square Garden. Mr. Brunson has been brilliant, averaging 39.2 points per game during the winning streak and leading the Knicks with his tenacious play.

Mr. Brunson “always wants to do more and get better and he wants his team to do well,” Mr. Thibodeau said. “He’s just a great player. He’s impacting winning in a great way. The numbers are staggering and the winning is winning, but to also have the humility to go along with that makes him enduring to the team and we’re lucky to have him.”

The surge coincides with the return of a crucial cog OG Anunoby, who was out for most of the second half of the season with an elbow injury. A defensive specialist, his versatility on offense has been a much-needed asset.

“OG is really coming and that’s a great sight for us,” Mr. Thibodeau said, adding, “I love the way he’s playing and his versatility, playing him at the three, four, or go small ball at the five,” meaning swing guard, forward or center. “You don’t lose any defense,” the coach said. “That’s what I love about him is his defense.”

Mr. Thibodeau deserves plenty of credit as well. A rash of injuries threatened to decimate the Knicks’ season. All-Star Julius Randle is out for the year with a shoulder injury that needs surgery. Center Mitchell Robinson also was out for an extended time with a bad ankle, and Mr. Anunoby was slow to return to the active roster. Somehow the Knicks are ending the year better than anyone could have expected a month ago.

“Everyone is playing well,” Mr. Brunson said. “I think the best part is when one person isn’t playing well we all know how to back each other up and make sure we’re on the same page where we’re giving each other confidence. It’s just the chemistry we have on this team. We don’t care about the credit. We just go out there and try to find a way to win.”

The Knicks, though, understand that the postseason is a different animal. The games are intense and the mistakes must be minimal. “I don’t want to see the same mistakes repeated over and over,” Mr. Thibodeau said. “I want us to understand there’s a difference in the fourth quarter. I want us to understand what it is to use good judgment in the fourth quarter. Those are the things you evaluate because you determine your rotation based on those things.”

Mr. Thibodeau pointed out the contributions of forward Josh Hart who’s “just a monster,” guard Donte DiVincenzo, who has averaged a steady 15.4 points per game, and sharp shooter Bojan Bogdanovic, who has found his scoring touch with 24 points over the last two games. The overall team chemistry has helped Mr. Brunson take his game to new heights.

Mr. Thibodeau said that “It’s a credit to him and his teammates because they all have to be connected. The double teams are coming fast and if one guy is not in the right spot, you can take advantage of it.”

Though the playoffs are almost here, the Knicks want to stay where their feet are planted and not get ahead of themselves. “We’re not worried about a ceiling or a floor,” Mr. Brunson said. “We’re just focused on getting better every single day.”