The Premier League champions suffered a shock 2-1 home defeat by CSKA Moscow on Wednesday and are now bottom of Group E with two games remaining.
Seydou Doumbia scored twice in the first half at the Etihad Stadium either side of a Yaya Toure free-kick as CSKA secured their first win against an English side.
Fernandinho and Toure were sent off in the second half as lacklustre City's European campaign reached a new low.
The hosts were furious that Pontus Wernbloom was not sent off for a second bookable offence when he pulled back Sergio Aguero, with Sergei Ignashevich cautioned instead by referee Tasos Sidiropoulos.
But City boss Pellegrini refused to use to pin blame on the referee for his side's flat performance.
He told Sky Sports News: "I don't think the sendings off decided the match, it was in the first half when we weren't ourselves.
"It is a crisis of confidence and we must find out why by talking to the players every day and working together."
City are two points adrift of CSKA and Roma with games against Bayern Munich, who are already assured of a place in the last 16, at home and then the Serie A side away to come.
Pellegrini has not given up hope that can pull off a remarkable turnaround and go through with pool winners Bayern.
He added: "You can never imagine you are out when the maths says you are still in. We must try and work hard and get back to our normal style of play."
