Just 10 days after thrashing Manchester United in a much-celebrated performance, City found themselves on the receiving end as they were crushed 3-1 by the Germans in the Champions League.
City contributed to their own downfall on a night of costly errors for the defence, and particularly goalkeeper Joe Hart, but there was no hiding from Bayern's mastery at the Etihad Stadium.
Pep Guardiola's side dominated possession and were quick and clinical, playing a brand of brilliant football to which City aspire.
Richards, who was unexpectedly recalled for the match after an injury-hit past year, said: "They have some outstanding players and they played us off the park.
"Sometimes you have to hold your hands up and say you were beaten by the better team.
"We want to play again quickly and get it out of our system.
"We are used to being better than everyone else. Without being cocky, we are used to playing nice football but we got taught a lesson.
"It is disappointing to be on the receiving end."
City were on the back foot from the seventh minute after Franck Ribery cut inside from the left and beat Hart with a long-range shot which the goalkeeper should have stopped.
It was the latest in a series of errors from the 26-year-old and concerns over his form are again being raised.
Hart was completely exposed for Bayern's second goal early in the second half as Gael Clichy switched off and allowed Thomas Muller to take a crossfield pass and round the keeper.
Fernandinho lost possession in midfield and Arjen Robben burst through to add Bayern's third moments later, beating Hart too easily at his near post.
Guardiola had opted not to play a recognised centre forward and instead packed the midfield with attacking players.
Richards admitted City failed to deal with that approach.
The 25-year-old, for whom the game was only his second of the season after making just eight appearances last term, said: "They dominated midfield. There were six in there and we couldn't cope with them.
"Before the game everyone was excited, wanting to play the best team in the world at the moment. They just showed why they are the best.
"But we thought we should have done a lot better than that.
"I think we knew of their quality before the game but sometimes, at home, you expect the boys to be a little bit better than we did."
The result took Bayern three points clear at the top of Group D and, in all likelihood, left City in a battle with CSKA Moscow for second place.
City now face back-to-back games against the Russians. They are due in Moscow in three weeks' time and host them at Eastlands in November.
Richards said: "We know Moscow have got some good players. We will go out there, roll our sleeves up and hopefully get a good result."
City's immediate task is Saturday's visit of in-form Everton, a side they have struggled against in recent seasons.
The Toffees have won six of their last eight against City and will also head to Manchester as the only remaining unbeaten team in the Barclays Premier League this season.
City were also beaten at Aston Villa last weekend and are anxious to bounce back.
Richards said: "We have had two disappointing results.
"We don't like to lose two games back to back. We have got a winning mentality built into us.
"We have to put it right on Saturday. We are at home and we will give a good performance and hopefully get three points."
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- Manchester United
- Joe Hart