The visitors took an early sixth-minute lead when Ángel Di María’s cross found Karim Benzema free in the City area, with the French striker producing an emphatic finish past Joe Hart.
Sergio Aguero came close to restoring parity midway through the second half but was denied by a world-class save from Iker Casillas’ before the Argentine scored a 71st-minute consolatory strike from the penalty spot.
“We didn’t lose [the campaign] tonight, we lost it in the first games – Madrid and Dortmund at home and Ajax away,” Mancini told Sky Sports.
“In Madrid, we were 2-1 up with five minutes to go, in Amsterdam we were 1-0 up and missed a chance to close the game.
“I hope it will give us more experience next year. I’m disappointed like everyone here but when we started this group, we knew it was going to be a difficult group.
“We are a good team but we went out and made some mistakes in this campaign.”
City remain in fourth place, a point behind Ajax, and Mancini turned his attentions to finishing third and a shot at winning Europe’s second-tier club competition.
“Of course I want to win the Europa League if it is possible,” said Mancini. “Of course I do.”
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.