Having Welker wouldn't have prevented the first 2 Baltimore TD's, and wouldn't have helped the team any on defense. Plus, with the Ravens barely covering Moss, they'd have devoted themselves to shutting down Welker. I don't think he'd have been a factor.
I think the biggest problem may be Belichick's ego. As the years have gone on, and he's lost coaches/staff, he's tried to take on more of the responsibilities. Calling defensive plays after Crennel left, running the offense after McDaniels left, and making personnel decisions after Pioli left. I think he needs these people. He may be an extremely intelligent coach, but he's not infallible, and he can't do everything. Time to bring some competent people in (bring back Romeo!), and redelegate some of that responsibility.
As for the on-field product, I agree with Rover about the Defense, but I think the offense needs some work, too. They need a second down field threat. I love Welker, but he's a short pass guy who can run after the catch (and really, he won't be around next year, and who knows how well he'll be able to play when he does come back - he makes a lot of quick moves, and if his knee isn't 100%, he might lose some of his ability to cut), and they need someone besides Moss as a deep threat. Aiken is TERRIBLE.
Probably even more important than that, though, is the running game. At the beginning of the year, the local talking heads claimed that the Pats didn't need a running game, which is simply stupid. They need to be able to run for three reasons: 1) to set up the pass; 2) to kill clock in the 2nd half; 3) to punch it in at the goal line. We've seen a number of 4th quarter collapses, in which the offense can't move the ball, only runs about 50 seconds off the clock, and puts the defense right back on the field. I'm oversimplifying, but the offense basically had three plays, either a short pass to Welker (sometimes Faulk), a deep pass to Moss, or a run up the middle.