The manager has been criticised recently for suggesting Liverpool and Manchester City were favourites for their matches, but he was in tubthumping mood before the home game with the European champions on Tuesday night.
"We know that on our day we're as good a side as any but we have to show it more often," Moyes said.
"I've got great belief in the players and I've said that from day one - that hasn't changed. I get the feeling the players all want to play, I can tell that from their attitude in training.
"They all want to play in the big games, that's what the players here have wanted to do over the years."
United, seventh in the Premier League, are the longest odds they have ever been for a match at Old Trafford, but Moyes says he has no fear of facing Pep Guardiola in the opposite dugout.
"I'm really looking forward to coming up against him," Moyes said. "I've no doubt I'll be doing it plenty of times in the future."
Asked why Guardiola has had so much more success, having already won the Bundesliga title, he said: "He had a year to get himself ready for the Bayern job."
Sitting alongside Moyes at the official press conference, Ryan Giggs took up the theme. "As players, we don't see ourselves as underdogs," the player-coach said. "We see ourselves as Manchester United, playing in the Champions League. It's two huge clubs, two great histories, two teams who play football the right way."
Moyes has injury problems in his backline with full-backs Rafael and Alexander Buttner now doubtful to feature while Rio Ferdinand, Chris Smalling and Jonny Evans work their way back to full fitness. "We have defensive issues undoubtedly so we will have to make one or two changes."
Shinji Kagawa, who has played Bayern Munich four times, winning all four, could retain his place in the side having started against Aston Villa on Saturday. "It's something we seriously consider. He is in our thoughts for tomorrow," said Moyes.
Moyes added that a degree of caution is required in the first leg. "We have to make sure both games are important but we'd love to go to Germany with a win under our belt."
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