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 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."