Let me try to give our universe a different explanation to the causation and here is my play by play.
Brady lost because his O line sux. He kept on getting pressured and sacked and if you pressured any qb who is a pocket passer, he will have a bad game. During one drive, think tb got like 7 straight flags. We saw on tv that brady was not happy on the sidelines so he went out and chewed his lines men. During one play when brady was sacked, we can see that he looked at the line man that couldn't blocked for chit and his eyes were mad dogging that poor kid.
So by now, you know that Brady's frustration is at an all time high. The last play of the game, it was 4th down but after he threw an incomplete pass, he raises his fingers up and calling it a 4th down. Looks like brady got so stressed and tensed that he forgot which down it was.
You know what players do after the 1st half is over? They run into their locker rooms. Brady probably confused that it was half time is my speculation to the funnies to why he did not shake hands.