Since Atlanta's offense wasn't on the field much, it means that Atlanta's defense was. And, by mid 4th quarter, they were exhausted.
While it is for different reasons, this is why the super fast paced, hi tempo style that Chip Kelly always wants to run might work early in games, but not late. The defense spends too much time on the field.
This is what constantly happened to the Rams under Fisher. The offense was so horrible that the defense was on the field way too much. So the second half looked entirely different than the first half.
Pats play a ball control offense with sustained drives. Their D isn't on the field so much that they're done by the 4th quarter. And the Pats have depth.
But add to that the just plain dumb play calling when Shanahan decided to keep his foot on the pedal instead of running and burning clock with a sizeable lead. And Ryan hanging on to the ball and not throwing it away when the goal was to protect a large lead. And not playing for a FG when they were at the 25, and with sacks and penalties they got backed up to the other side of the 50. Just poor play calling, poor game management and poor QBing at a critical time.