City were edged out on away goals in their last-16 tie despite a late comeback. The English side trailed 3-0 on aggregate after conceding goals to Matias Fernandez and Ricky van Wolfswinkel in an indisciplined first-half performance, but two goals from Sergio Aguero and a Mario Balotelli penalty gave City hope of an unlikely win which goalkeeper Joe Hart was close to completing.
Mancini said: "In the first half we didn't play, but I am the manager and it's not the players' fault, but mine - I probably made a mistake. The players did everything, and fought on the pitch. When a manager doesn't prepare well for the game, this happens."
He added: "When I lose a game I think about why I lost and think about where I made mistakes.
"I understand we have big players but in football every game is difficult, and in the Europa League and Champions League it is more difficult, because every team plays to win.
"Sometimes we make mistakes, but the manager is the person who always prepares the game, and I probably made some mistakes for these two games."
Mancini's comments were similar to remarks he made after an unexpected Barclays Premier League defeat at Everton in January, when he blamed poor preparation.
City now only have their title challenge to concentrate on and, after losing top spot in the table last weekend, must now look to get back on track against Chelsea next Wednesday.
Mancini said: "I am proud for the second half because we had a fantastic 45 minutes, but I am very sorry for the players and our supporters because they were fantastic in that second half. But I am disappointed in myself, not the players.
"For the second time this year, I hope I don't make mistakes against Chelsea."