So far, they've done a pretty convincing job providing answers.
The Eastern Conference leaders have won five consecutive games since the arrival of their new additions, a run they'll look to extend Wednesday night against the visiting Los Angeles Clippers -- the team the Celtics beat to begin the streak.
The reaction to Boston's decision to deal Perkins, one of its defensive anchors in the paint, was largely skeptical, and the Celtics (46-15) were among those that needed the most convincing. They played one of their worst games of the season hours after the trade, losing 89-75 at Denver on what Kevin Garnett called "a tough day to play basketball."
It's been a lot easier since Green and Krstic arrived to face the Clippers (24-40) two days later. Boston won 99-92 at Staples Center behind 24 points from Paul Pierce and 22 from Ray Allen, and hasn't lost since. The winning streak hit five with an 89-83 victory at Milwaukee on Sunday.
"We got a nice little rhythm, truthfully. It really starts with our core group," said Pierce, who's averaged 22.2 points during the streak. "At the end of the day we're finding a way to win."
Green's minutes have gone up the past two games and he's averaged 16.0 points -- up from 6.0 in his first three contests -- while Krstic has averaged 12.2 points while starting every game since the deal.
Krstic's play in particular has coach Doc Rivers smiling.
"He finishes so well and so much better than I knew," Rivers said after Krstic scored 17 against the Bucks. "He's really comfortable and the guys are very comfortable with him."
The Celtics are also working on incorporating fellow newcomers Troy Murphy and Sasha Pavlovic in the rotation, while guard Carlos Arroyo -- signed Monday after being released by Miami -- should be available for this game.
Glen Davis, meanwhile, is still at least two games away from returning from left knee tendinitis.
Boston's offense has gotten sharper since the trade. The Celtics have averaged 103.4 points and shot 42.2 percent from 3-point range during the winning streak. In their previous 12 games, they averaged 91.3 points and connected on 30.7 percent of their attempts from beyond the arc.
The Clippers didn't have Eric Gordon when they faced Boston last month and won't have him Tuesday, either. Los Angeles' leading scorer missed six weeks with a right wrist fracture before returning in a win at Houston last Wednesday, but he aggravated the injury in Saturday's victory over Denver.
Gordon is out indefinitely.
His teammates shot just 41.9 percent without him Monday at Charlotte, but were able to open a five-game road trip wit a 92-87 victory.
It's the fourth three-game winning streak for the Clippers, who haven't won four in a row since Dec. 31, 2009-Jan. 10, 2010.
"It's great to get a road win like this," said Blake Griffin, who had 17 points and 15 rebounds. "We've struggled on the road, so it's good to get a win to start it out. It's good to kind of get the confidence going and hopefully we can build from here."
Los Angeles, 6-25 away from Staples Center, has lost its last three trips to the TD Garden.
All five of the Celtics' home losses, however, have come against Western opponents.