The defending Premier League champions found themselves a goal down in the opening stages after Martin Demichelis lost his marker, before Yaya Toure equalised with a lovely free-kick.
However, England No 1 Joe Hart was poorly beaten at his near post, Seydou Doumbia scoring his second of the night, and from there City went to pot.
Manuel Pellegrini made two half-time changes but one of those, Fernandinho, managed to pick up two yellow cards in just 25 minutes and City were down to 10 men.
Chasing the game Toure then turned villain, needlessly lashing out to be shown a straight red card.
City had chances and Sergio Aguero had a late appeal for a penalty waved away, but the home side were simply not good enough on the night.
Who were there best and worst performers? Scroll through the gallery below...
Manchester City 1 CSKA Moscow 2 - player ratings
Show all 12
Disagree with out ratings? Let us know in the comments...
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies