You had to do a pass play in order to play 4 downs. You had to play 4 downs to maximize your chances to win the football game. If you had to do a pass play, you do it on second down, again to maximize your chance to score. On first down you try to pound the rock with Lynch because of course it was. You're on the half yard line and the other team has hardened its defense about as far as it can. If you pound the rock again on second down and don't get in, they just built their confidence for third down, which almost has to be the last play of the game with that little clock left. Suddenly the whole drive becomes a coin flip -- unacceptable.
Meanwhile, if you can catch your opponent by surprise with a well executed pass, you stop the clock if it doesn't work and score if it does. Then you have 2 plays to try to ride Lynch to score.
Two problems
1: The Patriots were not caught off guard
2: The execution of the pick was horrible in every possible way.
Carroll is at fault for two things. First, the Seahawks were disorganized and unfocused both in clock management and in execution. Clearly his team was not well briefed. Second, he probably should have exploited the suspected anticipation of a run with a play action pass, draw defenders to the left and open holes for Lockette and Kearse. Misdirection is key to a pass like that on the goal line. Instead Wilson was literally telegraphing the play from the moment the ball was snapped to him.
The play was not well executed, the team was not well briefed or focused, after playing a good 59 minutes they basically got eaten for lunch by the crunchtime butterflies. Give Pete Carroll all the stick you want for that. That's fair criticism of a head coach. That's the sort of thing he SHOULD be criticised for by knowledgeable fans. The play call was fine, at the very least there's good reason why to consider running that play. The problem is not the play, it's that the play was executed poorly, with little discipline and no thought for deception or misdirection, and that gave Butler room to make the defensive play of the decade. The team was not ready to make the play they needed to make, that's directly on the head coach. That's actually a far harsher criticism of Carroll than one ill timed bad play call.