Samir Nasri opened the scoring against the run of play in the 23rd minute, with the France international finishing off a sweeping City counter-attack.
However, Siem de Jong levelled for Ajax with an emphatic strike before half-time and Niklas Moisander’s header put Frank de Boer’s men ahead in the 57th minute.
City’s misery was compounded when Christian Eriksen added a third for the home side, but despite a poor display from his players, Mancini accepted full responsibility for the loss.
“They played better than us,” said Mancini. “It’s my fault because I could have prepared better for this game. I didn’t prepare the players well for this game. The defeat is my fault.”
He added: “I thought in one way and the game was different.
“We didn’t [underestimate Ajax] but when you prepare for a game and you think in one way to play in a certain way, but then instead it is a different game – it’s difficult.”
With Borussia Dortmund beating Real Madrid, Mancini admitted it will now take a “miracle” for the Premier League champions to reach the last 16 with his side now bottom of Group D on one point.
“It is going to be difficult [to qualify], very difficult. There is one team with seven points and one with six and one with four. It would need to be a miracle like last year.”
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