While Belichick shouldn't have decided to go for it in 4th and 2 at the end, they did make it across the 1st down line. The ball was spotted incorrectly. I'm not the only one to think this.
I think it was a fair ball game until it came time for the refs to call that play at the end, and they decided to "cheat" a little bit. Because the Patriots had no time outs left, they couldn't challenge the ruling. So the refs could spot the ball a yard short and no one would be the wiser since they only played the replay where you got to see the guy holding the ball ONCE.