One timeout. 40 seconds. Do I agree with it? No but it's easy to play MMQB.
Belichick not calling TO kind of forced Carroll's hand.
With 40 seconds left he needs to get three plays in to maximize his chances. He has one timeout, so if he runs on 2nd down he can't stop the clock if they miss on both 2nd and 3rd down, MAYBE denying them a 4th down attempt.
But if he passes JUST ONCE with his QB who has been very good overall in the playoffs, he likely gets a clock stoppage after 2nd down and can call timeout after 3rd down, setting up a do-or-die 4th down. He basically maximizes his chances-- two runs plus a high-percentage pass.
Only Belichick was ready for the pass, and was hoping for it by NOT calling timeout, having even his 4th string CB ready for that play in particular.
All in all, a brilliant awareness of situational football and one of the biggest reasons this guy is maybe the best ever to have the job.