Arjen Robben hit out at United's approach to the first-leg.
"If you look at the recent history of the Champions League, you can see when teams sat back, waited and waited and got something from games and got through," says Moyes.
"So I don't think there is any shame in what we did at Old Trafford, not by a long way. Tactically, we played very well on the night but we might need to think differently in the second leg.
"A change of strategy is something I'm looking at. Pep will probably alter things and use players in different positions. We have a decision to make as well and that's something I'm mulling over.
"We have to try to get the first goal in Munich because that would put us in the driving seat. It doesn't have to be in the first minute but we need it somewhere in the game.
"We don't want to concede first and feel that we have to go chasing the game. That could be a very difficult thing to do against Bayern because they are so good with the ball. It's such a big prize and we are going to try everything we can on the night to get through to the semi-finals."