United's collapse after the Frenchman's thunderbolt illustrated all their weaknesses in their first season under David Moyes.
Moyes said his focus was on building a team to get Manchester United back in the Champions League.
Title holder Bayern came alive in the second half after falling behind and beat United 3-1 (4-2 aggregate) to advance to their third straight Champions League semi-final.
Bayern's poor recent home record against English opposition have made United's task a lot less daunting than it was when the draw was made.
United are in desperate need of Rooney's power and finishing ability in Munich as they look to improve on a 1-1 home draw in the first leg.
Holders Bayern have a slight edge after a 1-1 draw in Manchester last week but Guardiola warned of the English team's defensive tactics and their appetite for quick breaks.
Mata inspired United to a 4-0 victory at Newcastle, securing a 10th away win in the Premier League that belies the champions' poor home form.
Wayne Rooney has also been ruled out of Saturday's Premier League game against Newcastle United.
Former Manchester United manager Ferguson will be swapping the dugout for the lectern after agreeing a long-term teaching position at Harvard University.
Ten points behind fourth-placed Arsenal with only six League games left, United seem certain to miss out on a Champions League place next season.
Bayern host United next week in the return leg of the Champions League quarter-final with the Germans favourites to advance.