The Premier League champions went down 3-1 at the Amsterdam ArenA in their Group D fixture and are still looking for their first win in the competition this season.
"They were better than us," he said. "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. We change for five minutes to three at the back, but we always have 11 players."
Mancini added that it will now be "very difficult" for City to progress beyond the group stage.
"It is very difficult to qualify now," said the Italian. "It would be a miracle."
In the other game in Group D, Real Madrid lost 2-1 at Borussia Dortmund.