Several reasons. Most of all, the Saints were playing behind for most of the game(actually, they never had the lead).
On the first drive, the passing game was working. But then as the 1st half progressed, the Bears jumped out to that 16-0 lead. They were attempting to run on the Bears, but I didn't think they were having much success. The Saints best running occurred this year when they crossed teams up. Pass a lot at first and use Reggie Bush a lot in motion, which left the middle open to the run. But the Bears are no ordinary team. They have excellent DL and LBs. The Saints could not win at the point of attack.
Now, I do question the play call of Brees passing out of his endzone when the game was 16-14. It defintely backfired on the Saints. However, with the great job that Payton did this year with the playcalling(and the entire team), I will not question his tactics.