City's haul of just three points from six games was the worst performance by an English club in the Champions League group stage with Mancini's men finishing bottom of Group D and failing to qualify for the Europa League as well.
Newspaper headlines on Wednesday spoke of City as "The Worst Ever" and dubbed them "£320m flops".
Mancini saw a silver lining in Tuesday's 1-0 defeat to Borussia Dortmund, however.
"Clearly this can help us win the Premier League because we don't play in the Europa League," he said. "But getting into it was our target. We wanted to win."
City are currently second in the Premier League, three points behind Manchester United and seven clear of third-placed Chelsea, the European champions who are in danger of going out of the Champions League on Wednesday.
United, who travel to City for a league derby at the Etihad Stadium on Sunday, have already secured first place in Champions League Group H.
Had City qualified for Europe's second tier competition, which awaits the third-placed clubs after the Champions League group stages, they could have faced up to nine further European matches on top of domestic fixtures.
"I'm not embarrassed about where we have finished or the points tally," said Mancini of City's failed European campaign and second successive exit at the group stage.
"There could be embarrassment if we had not played with 100 percent effort. You can still play 100 percent and lose, and that is what happened."
Mancini recognised that City needed to regain their sharpness in front of goal after scoring just seven times in six group games.
"At the moment we are not scoring goals, certainly not like we were last season. We are creating chances but we are not scoring," he said.
"That is a big problem that we need to work at."