The Premier League champions’ second consecutive group-stage exit was confirmed on Wednesday night thanks to a 1-1 draw with Real Madrid – only City’s third point from five games in the competition.
The 47-year-old admitted he is disappointed with the failure to advance given the talent in the squad and is now keen to right the wrongs domestically.
When asked by Sky Sports if the club’s owners would be aggrieved with the team’s failures in Europe, Mancini replied: "No. We knew it was a difficult group. But we had a good team, when you lose against Madrid and Dortmund you are disappointed.
"I am disappointed like everyone here but also when we started this group we knew it'd be a difficult group. We are a good team and we went out and we made some mistakes.
"The fans are fantastic. They understand we are disappointed like them. They are really important because the season isn't finished. We are top of the league, we have the FA Cup. Now it's finished we can do nothing."
Unlike last season, when it snatched 10 points before being knocked out, City is yet to register a win in the competition, and Mancini rued mistakes in previous games – namely the two late goals conceded against Real Madrid on matchday one.
He continued: "I think that we didn't lose tonight, we lost in the first few days. Madrid, and Dortmund at home. It was a different game but 2-1 with five minutes to go.
"In Amsterdam, we scored, but we were missing one or two chances to close the game."