Honestly there was no logical reason to punt in that situation that I can think of.
The score dictated that you needed a play
The distance dictated that you had a higher probability of making it, QB sneak, power run, hell even a Nagy special
The momentum had shifted and we needed a play to get it back
The time left in the game dictated that you needed to steal a possession
Finally, the most blatant reason, Rogers was picking your defense apart after second half adjustments, and your decision to punt was putting the ball back in his hands...
Last week I watched John Harbaugh decide to go for a two point conversion to either win or lose the game (could have tied and went into OT)against the Steelers. The attempt failed and they lost, but every rational person, said two things:
1. That was a gutsy call, that showed he believed in his players
2. He took matters into his own hands, and his decision was based upon controlling the outcome of the game and not relying on a coin toss and his struggling defense.
John's decision was solid despite the outcome, just the opposite for Nagy