While the bigs (particularly Davis, who was horrible) need to do a much better job rebounding the ball, I think the bigger problem last night was with the perimeter guys. When the C's are at their best, Rondo and Pierce in particular have a lot of rebounds.
The C's system really relies heavily on the perimeter guys to defensive rebound, because they ask their bigs to spend so much time blitzing the perimeter (its even worse against a team like the Knicks with such good spacing). However, last night, they were not crashing down at all, and instead were leaking out.
Now, this certainly helped their offense, and Rondo in particular had more than a handful of easy baskets because of his leaking out. However, particularly when they didn't have both KG and JO in there, this was a major reason why they kept losing the rebounds.
With the Knicks, who shoot a ton of long jumpers, there are a lot of long rebounds, and those become easy pickings for the offense when the other team is already leaking out.
Next game is going to be really interesting to see what Doc does about this. Will he sacrifice some of the fast breaks in order to lock down on the rebounds? Personally, I think they need to find some sort of balance. But this is going to be a real challenge for game 3, since it will be a VERY hostile environment, and the energy in the building will be through the hoop.