Long answer: what game were you watching? Rodgers gave them as best of a chance as they had. The Packers lost mostly because of one reason: they didn't EXECUTE. Even with the horrible officiating calls, the Packers managaed a way to shoot themselves. If the Packers just manage to hold on to/catch the football, the score could have just as easily been 31-20 in favor of the Packers.
The only play I can think of that resulted in a turnover that wasn't a result of Green Bay just shooting themselves was the Osi strip sack on Rodgers. Rodgers gets that pass off just a split-second sooner, that play goes down as a touchdown due to blown/poor coverage because Jennings(?) was WIDE OPEN. Then again, the Packers were dropping passes all night, so who's to say Jennings wouldn't have dropped that one.
Rodgers single-handedly kept a number of those drives alive because when his receivers were blanketed, he made plays on his feet to save the drive. I think Rodgers played an outstanding game, but the Packers as a team didn't execute. The miscues in this game had NOTHING to do with who was behind center.