Penalties are part of the hidden yards in football. When I look back at how they could have lost on Monday night when the Green Bay Packers had over 100 yards more in total offense (379 to 276) than the Bears, and had the ball for ten minutes longer (35:49 to 24:11), the answer can be the hidden yards lost due to penalties and special teams (touchdown WR Devin Hester!).
The special teams performance was awful, and I don't know if they truly intended to punt the ball away to Hester because P Tim Masthay is more of a big leg punter than a directional kicker. Actually, does he have any idea where the ball is going? But that will be worked on in practice, and while it won't ever be perfect, it usually isn't as bad as it was last Monday either.
As far as the penalties go, Mike McCarthy was upset, but not that upset. He said there some penalties that "you just have to live with." He referenced LB Frank Zombo's personal foul specifically, but he didn't seem all that upset at his offensive line either. Greg Bedard spoke with CB Charles Woodson after the game, who was upset that a penalty was even called on rookie SS Morgan Burnett as both players went for the ball. Woodson is certainly one player who has never shied away from an aggressive play (and had one pass interference penalty early in the game), but probably wouldn't have as many game-changing plays of his own if he was always worried about penalties. Obviously they never help, and the hidden yards can add up against you, but I can't recall a game where it was decided by a bad penalty. In the loss last Monday, I'd focus on the two big punt returns, and the long pass plays to WR Johnny Knox, first.
Do you want to see the Packers dial down their aggressiveness to some extent to avoid some penalties?