Matt Glassman makes clear why Belichick was right to let the Giants score even though the Patriots lost:
[W]hich is more probable — missing what amounts to an extra point, or Tom Brady leading a touchdown drive in 1 minute with two timeouts?…League wide, 99.4% of extra points were made this year. The Giants were 45 for 45. You think Brady has less than a 0.6% chance of leading a TD drive with a minute and two timeouts? Not a chance. According to the NFL win probability stat, the Pats had a 4% chance to win when they got the ball back. And they only had 1 timeout as it turned out. Here’s the thing: football is a zero-sum game. If Belichek was correct to let the Giants score, then by definition the Giants were wrong to get into the end zone there. By the above math, the Giants gave the Pats a 25-1 chance to win, when they could have made it a 199-1 chance. That’s right: by getting in the end zone, the Giants increased their chance of losing eightfold.