In my opinion the Celtics struggles have been mental. You are right that Perk didn't play much and for that matter, neither has either O'Neal. But they kept winning. I think the trade for whatever reason has affected the team's focus. It may even be subconscious, but they aren't focusing on team play any more on either end of the court.
1/3 of the team has been changed and they are working 5 new players into the team both on offense and defense. Some of those guys just haven't gotten it (See Murphy, Troy) and some are doing very well (See Green, Jeff) and some have been up and now are down (see Krstic, Nenad). The bench seems to be coming along fine, and that's where most of the new guys are.
But it's the starters who are struggling. And we can't even blame Krstic, who has been struggling as well because the unit that lost the lead and game to the Bobcats was the Big 4 and Baby and that same unit has closed many games.
All that being said, I do believe that the trade is to blame for the slump. It's different from last year. Doc never called the team soft or selfish last year. He never got frustrated with the team like he has this season. It's not just laying back and waiting to get healthy and waiting for the playoffs like last year. I think that having to say good bye to Perk and 4 other players took a toll on their psyches and on them mentally. I think this is particularly true of Rondo. Maybe he subconsciously doesn't believe the team is as good without his best friend in the middle and just is going through the motions.
During this stretch they have abandoned team ball on both offense and defense. They no longer move the ball and find the open man. Each player is trying to do things individually. They are not covering for each other on defense. There have been times when they focus and we see what the team that we have now is capable of - against the Bucks and down the stretch vs the Knicks for example.
This team is the same team that virtually shut down the Bucks. They also mounted 2 furious comebacks that showed how they can play if they want to. But it's mental and if they can get past the mental hurdle that has been causing this lack of chemistry and team play, they will once again be a dominant team. They are strong enough to do it and smart enough to figure out how.
KG,Pierce, Rondo and Ray are the heart of the team but Perk was the pacemaker, whether he was on the court playing or on the sidelines cheering them on and shouting out encouragement. Doc will help them get their hearts straightened out again and they will once again be the Celtics team that surged to the top before the trade.