The result leaves Bayern with an away-goal advantage heading into the quarter-final second leg at the Allianz Arena, but Moyes is confident his side can still progress to the semi-finals.
"We know we've got to score a goal," he told ITV Sport. "At the moment if the score stays the same, Bayern are through. We've got to do something about it.
"I think tonight we said that we wanted to go into the next leg with a real chance - a fighting chance - I think we've done that.
"We've given ourselves a great opportunity to try to go to Munich and get a victory."
Moyes also said referee Carlos Velasco got two crucial decisions correct, first deciding not to show Antonio Valencia a red card, before dismissing Bastian Schweinsteiger with a second yellow for a foul on Wayne Rooney, ruling the Germany international out of the second leg.
He added: "I've had a look at them both. The boy [Alaba] tackles the ball on to Antonio Valencia, they both make a tackle, they get up, he gets there first.
"I think if anything it's just Antonio's follow through, but it wasn't given.
"I think Schweinsteiger trips Wayne up so I think it looks like a booking or if not it's at least a foul."