United ended a difficult week on a high on Saturday when they beat Aston Villa 4-1 at Old Trafford.
The match, which was overshadowed by an airborne protest against manager David Moyes, boosted morale following the 3-0 defeat to Manchester City in midweek but the Scot knows Bayern will pose a much stiffer test when they come to Old Trafford next Tuesday.
Pep Guardiola's stellar team have had little trouble progressing to the quarter-finals of the Champions League and they won the Bundesliga with seven matches to spare.
Mata was part of the Chelsea team that defied the odds and beat Bayern to lift the Champions League trophy in Bavaria two years ago though, so he thinks United should not be fazed by the prospect of facing the unbeaten German side.
"I lived something like this in my first year at Chelsea," the Spaniard told United Review.
"Things were not good in the Premier League but we won the Champions League, so why not (again)?"
Mata scored his first goal for United against Villa following his £37.5million move from Stamford Bridge.
The midfielder will be unable to repeat the feat against Munich though as he is cup-tied having played in the competition earlier this season with the Blues.
The Spaniard will be in the stands to support his team-mates for Tuesday's first leg, but he concedes the experience of watching United from afar has been a tough one at times.
"It's very frustrating not being able to play," said Mata, who was also part of the Chelsea team that won the Europa League last season.
"It's very nerve-wracking when you are watching from the stands.
"I was suffering in the last 15 minutes of the second leg against Olympiacos (when United needed to hold on to a 3-0 lead to progress).
"It's a shame I can't play but I will support my team-mates in every game we have in the Champions League, hopefully up until the final."
With the likes of Bastian Schweinsteiger, Mario Mandzukic and Arjen Robben in the team, it is little wonder Bayern are favourites to retain the prize they won by beating Borussia Dortmund at Wembley last May.
But rather than fear the Germans, Moyes cannot wait for the contest to begin.
"I'm really looking forward to it," said Moyes, who is a self-confessed admirer of the Bundesliga.
"It will be a tough game. They are probably the best team in Europe at this moment, but bring the challenge on.
"Coming to Old Trafford isn't an easy place for any team."