City surrendered a lead to crash to a 3-1 defeat at the Amsterdam ArenA which left them bottom of Group D with three matches to play.
Mancini cited poor preparation as he looked to deflect attention from the disappointing performance of his players.
The Italian said: "They were better than us. They played better football.
"It is my fault, I didn't prepare well for the game and I take the blame.
"I thought in one way and it was different. When you prepare in one way and it is a different game it is difficult.
"We had more chances to score and in the Champions League you need to score. It is my fault, I repeat."
City started sluggishly in the Dutch capital but took control with a fine Samir Nasri strike.
They failed to build on their lead and were pegged back by Siem de Jong before Niklas Moisander and Christian Eriksen, with aid of a deflection, made sure of victory for the hosts.
Mancini varied his tactics and formations as he chased the game and at one stage had Gael Clichy, who had the unlucky final touch on Eriksen's strike, playing in an unfamiliar centre-back role.
He said: "We changed for five minutes to three at the back, but we always have 11 players.
"I don't think that is important - three, four, five, six or seven defenders.
"If someone wants that as an excuse than OK, but it's not the reason.
"It is very difficult to qualify now. It would be a miracle."
Ajax coach Frank de Boer felt his side were worthy winners.
The former Holland defender said: "The most important thing was to show we have confidence in our own qualities and that is what we did in the first half.
"It was tough to be 1-0 down but in a fantastic moment we scored an excellent equaliser.
"At the break we warned the team to stay focused and sharp because City are dangerous and that is what we did.
"They carried on playing with the confidence and belief in our qualities.
"Although City had chances I think we deserved to win this game.
"This is the way we want to play football and I am proud of the team.
"We also need to play like this against Dortmund and Real Madrid."
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