If he admitted it at the time, the choice for the NFL would have been to either fine him or suspend him for the Superbowl. And there's no way they would have suspended him for the Superbowl.
There's no "smoking gun" that Brady told them to deflate the footballs lower than the required amount. However, there's a lot of circumstantial evidence that points to that conclusion. You've got the texts from the two employees, one of whom refers to himself as "the Deflator", that seem to indicate that Brady knows what's going on, if not involved himself. That makes sense. He'd have to know what's going on. He's the QB. He's the one handling the football the most. He'd know if the balls weren't up to specs if it were done without his knowledge.
In addition to the texts from the employees, you've got Brady refusing to hand over his cellphone and emails, when EVERY other person in the Patriots organization agreed to do so. Doesn't mean he's involved, but it's certainly enough to raise suspicion. There's no smoking gun, but there's enough evidence to say that it's "more probable than not" that Brady (at the very least) knew what was going on.
In addition, the investigation also found that it was "more probable than not" that this wasn't a one time event. Yeah, using deflated footballs for half a game in a 45-7 blowout isn't a big deal. But if I read yesterday's N&O correctly, the NFL believes this might have been going on since the beginning of the 2014 season. If that's the case, then the suspension + fine + loss of draft picks is appropriate.
It probably also doesn't help that the Patriots have the "repeat offender" status attached to them, after Spygate. Not sure why the Patriots feel the need to bend the rules to win, considering they're likely good enough without doing so, but if they continue to do so (allegedly), then they can't really complain about the punishments when they get caught.