The Packers have been able to pick up chunk plays when Rodgers has had time to scan and locate options down the field, as well as off of play action when the running game is working.
The early fumble and quick SF score put them down quickly and made it harder to stick to and establish the run. And without the running game, the PA game was not as effective. The pass rush of the 49ers made it extremely difficult to find downfield options. Sometimes Rodgers had no time, sometimes he had time and no one opened up, sometimes people came open and he missed them.
Thus the Packers had to rely on the quick passing game. But that plays into the weakness of Green Bay's personnel. We have very few players who are threats to create after the catch. Aaron Jones can, but that's about it. Adams is OK, but it's not his strength. Allison, Graham, MVS, Lazard, Kumerow... none of them are what you would call explosive in a short area. They're all either striders or just plain slow.
So the game script and opponent forced the team into an approach that plays against their strengths, and the results were predictable.
I think this was illustrated most vividly in the play that Collinsworth pointed out of the 49ers ignoring Graham. Graham ran out to the flat at the beginning of a running play. In theory, this is supposed to draw off attention in the case of an RPO or play action pass. He was totally ignored. Because Jimmy Graham catching the ball in the flat, even if he's wide open, is probably an 8 yard play at most. So who cares?