Joe Hart fumbled Franck Ribery's seventh-minute shot to break the deadlock, before Thomas Muller and Arjen Robben put the result beyond doubt early in the second half.
Despite a late consolation goal from Alvaro Negredo, the Bavarian outfit boasted 66 per cent of possession and Richards had admitted City's midfield was overrun by their superior opponents.
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"The midfield got dominated today with the six in there. We couldn't cope with them, and obviously Ribery and Robben were outstanding as well.
"At home you expect the boys to do a bit better than we did. We let them dictate the tempo of the game. It was a difficult day for us because we thought that we should have done a lot better."
Whilst highlighting his own teams failings, the defender noted the quality of the opposition and is keen to make amends for the performance against Everton on Saturday.
"Before the game everyone was excited and wanted to play the best team in the world at the moment, and it just shows you why they are the best," he continued.
"They've got some outstanding players and they played us off the park today. Sometimes you've just got to hold your hands up and say you were beaten by a better team.
"We'll look forward to Everton and try and get a result then."