Borussia Dortmund top Group D with seven points after beating Real Madrid 2-1, who have six points, in Wednesday night's other match.
Mancini's City now prop up the group with one point while Ajax are on three and are favourites to qualify for the Europa League after Christmas.
The Manchester City manager was not in a move to offer a defence of his team's shortcomings with City tactics of moving to a back three cited as a weak spot in the Dutch capital. He said: "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."
Mancini concedes it will take a "miracle" to qualify to avoid elimination at the first stage for the second successive season as goals from Siem de Jong, Niklas Moisander and Christian Eriksen cancelled out Samir Nasri's opening goal at the Amsterdam ArenA.
"It is very difficult to qualify now," said Mancini. "It would be a miracle."
He added: "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 then okay, but it's not the reason."