The NFL released information on which teams received Compensatory Draft picks in the NFL Draft and, unfortunately, the Patriots didn't receive any. Compensatory picks are given out to teams who lost better free agents than they acquired. "Better" is defined as a player who receives a larger contract and sees more playing time.
The Patriots lost DE Jarvis Green and TE Ben Watson to free agency, but Green was released just as the season started. Watson was the best receiver on the Browns, out of his tight end position, but his value and contract wasn't enough to outweigh the contributions of the free agent arrivals of the Patriots.
The Patriots acquired TE Alge Crumpler and DE Gerard Warren (Note: Warren was cut by the Raiders and does not count to the compensatory math) during the free agency (as well as an assortment of other players, but these are the two who really played well and stuck around). Both players were team leaders and integral members of the Patriots' squad.
A team who acquires and loses the same quantity of free agents is only qualified for a 7th round compensatory draft pick, but the powers that be deemed the value of Crumpler and Warren (as well as the other players added during free agency) far outweighed the loss of Green and Watson.
The lack of compensatory picks leaves the Patriots with nine (9) draft picks, with six (6) in the first three rounds. However, Belichick loves his late round picks, so you can be certain that he'll be trading around to pick up at least another 6th or 7th round pick.
Hill Note: I actually question if the Patriots were even eligible for any compensatory draft picks. The Patriots signed a lot of free agents (Warren, Damione Lewis, Torry Holt, Marques Murrell, Alge Crumpler, etc) and they only lost Ben Watson and Jarvis Green. Teams don't qualify if they picked up more FAs than they lost. This could be why the Patriots didn't receive any picks.
Hill Note 2: Here's the reasoning: Teams that add and subtract the same number of free agents cannot receive anything greater than a 7th round compensatory. The Patriots added Marques Murrell and Alge Crumpler, while they lost Jarvis Green and Ben Watson. Murrell and Green did nothing for their respective teams (and both were released) so they cancel out. Crumpler and Watson also cancel out because Crumpler's blocking balances with Watson's receiving. The powers that be decided that those qualities were equal enough that the Patriots didn't deserve a compensatory pick. Sounds fair to me.