It was minutes — no more than 15 — after the Hawks’ playoff series-clinching victory.

A first-round win over the Celtics on Thursday had just earned the Hawks a rematch with the Cavaliers, the opponent that swept to victory in last season’s Eastern Conference finals. That’s when Hawks coach Mike Budenholzer already had been asked about the tall task ahead. He chose to give himself and his team a little more time to enjoy what they all had just accomplished.

“We just won Game 6 in Boston, so I don’t have any thoughts about Cleveland,” Budenholzer said at his postgame news conference. “We’ll start preparing, but we might actually take a second to enjoy tonight. Our guys will be ready. I can tell you that.”

The Hawks dispatched the Celtics with a 104-92 victory in Game 6 at TD Garden to win the series 4-2. It was the Hawks’ first series victory over the Celtics in eight tries since the franchise moved to Atlanta. The clincher also was their first playoff win in Boston since 1988. Those were notable achievements for the organization.

The conference semifinals matchup will start Monday in Cleveland. Last year, the Hawks were the No. 1 seed in the conference after a 60-win season. This year, the Cavaliers hold the distinction of top seed.

“It’s a rematch from last year,” Kent Bazemore said. “They swept us. We definitely have a chip on our shoulder about that.”

The Hawks enter as the fourth seed after a 48-win campaign. A loss in their regular-season finale dropped them a spot in the standings that would have avoided the LeBron James-led Cavaliers for another round of the NBA postseason.

Members of the Hawks organization lament a number of bad losses during the regular season. They lost two games each to the Magic, Knicks, Bucks and Timberwolves and games to the Suns and Kings, all sub-.500 teams. The worst loss came the first game back from the All-Star break when they lost at home to a Heat team missing Dwyane Wade, Chris Bosh and Hassan Whiteside. That loss ultimately cost the Hawks the Southeast Division and the third seed.

Still, several players insist the Hawks are a better team this season despite the disparity in the win column. They are largely intact from a year ago, with only Bazemore replacing the departed DeMarre Carroll in the starting lineup. Defensive wing Thabo Sefolosha is healthy after missing the postseason with a broken right fibula. Kyle Korver is finally fully recovered from a pair of summer surgeries, one a season-ender on his ankle suffered in Game 2 of the series with the Cavaliers.

“I think we are a better team than last year,” Korver said. “I really do. Our identity is more on the defensive end than the offensive end. We know that we are going to have to play really well to beat (the Cavaliers). Our defense is going to have to be what it was in this series, if not better. Our offense is going to have to be a lot better. They are a great team. They have a lot of individual talent.

“It’s going to be a tough challenge. We are excited about it and will be ready to go on Monday.”

The Cavaliers won all three regular-season games against the Hawks this season, including two games in a 10-day span in early April. One of the losses was a two-point overtime defeat April 1 in Atlanta. The Cavaliers’ average margin of victory was 10 points.

The task now at hand is indeed tall.

“I’m excited to be in this position,” Al Horford said. “You work to be able to be in the playoffs, and we obviously just played a really good Boston team, and we have a big challenge ahead with Cleveland. We’re excited about it. Looking forward to getting started.”