The Premier League champions slumped to a 3-1 loss away in Amsterdam, which leaves their chances of advancing beyond the group stages in the balance.
Despite a lacklustre display from his side, Mancini took responsibility for the result:
“I think they played better than us, they played better football,” he said to SkySports after the game.
“Probably, it is my fault because I did not prepare the players well for this game and I am at fault for the defeat.
“I thought in one way and it was very different and probably for this reason (we lost).”
The City boss also confessed that getting into the final 16 will be problematic:
“I think that it is very difficult (to qualify), very difficult.”
The Citizens took the lead early on through Samir Nasri, but a Siem de Jong effort on the stroke of half-time levelled the scores.
Ajax then took the lead in the second period through defender Nikolas Moisander, before Danish starlet Christian Eriksen completed the scoring.
The defeat, coupled with Borussia Dortmund’s win over Real Madrid leaves City some way adrift of the top two slots in the group.
The Manchester club will host the Dutch side in their next European game.