The English league winners ended up with only nine men in their disastrous display at the Etihad Stadium.
Seydou Doumbia got the Russians’ two goals in the first half either side of Yaya Toure’s superb free-kick strike.
But after the break Fernandinho and Toure were sent off as City crashed to a defeat that leaves their Champions League hopes hanging by a thread.
They have only two points from four games and prop up Group E.
Afterwards a shocked Pellegrini said: “It’s very difficult to understand why we played so badly.
“From the beginning we were so nervous and we gave them two goals. Really, we didn’t play.
“In the first half especially, we didn’t see the team we normally see.
“We didn’t shoot once at their goal, we just had Yaya’s free-kick, and we gave away two easy goals.
“It’s hard for me at this moment to understand why it happened.
“I don’t think it’s just the Champions League.
“For the last two weeks we have not been playing the way we normally do.
“It’s a crisis of confidence. I don’t understand why but we must find a reason for it.
“We must talk with the players every day and try to win again.”
Pellegrini would not be drawn on the two dismissals, saying simply: “It’s the referee who has to decide about that.”
Doumbia capitalised twice on City’s terrible defending to score.
His first goal came in only the second minute when the Ivorian striker took advantage of a free header from a corner.
Toure equalised with a well-struck free-kick from the edge of the box five minutes later.
But Doumbia cashed in on a Gael Clichy error to race through and fire the winner into the bottom corner after 33 minutes.
Half-time substitute Fernandinho was sent off midway through the second half after picking up his second booking.
Then Toure was shown a red card for lashing out at a CSKA player to complete City’s awful night.
They are two points behind CSKA and AS Roma, who have four points. Out in front on 12 points and already through to the knockout stage is Bayern Munich, who beat the Italian side 2-0 last night in Germany.
Franck Ribery and Mario Gotze got the goals for Pep Guardiola’s side.
Also through are the Bayern boss’s old team, Barcelona, who beat Ajax 2-0 in Amsterdam.
Both goals were scored by Lionel Messi, who is now level with the Real Madrid legend Raúl as the joint all-time leading scorer in the European Cup. He has netted 71 goals in the competition.