City were edged out on away goals in their last-16 tie against Sporting despite a thrilling late comeback at the Etihad Stadium.
The English side trailed 3-0 on aggregate after conceding goals to Matias Fernandez and Ricky van Wolfswinkel in an indisciplined first-half performance.
Yet two goals from Sergio Aguero and a Mario Balotelli penalty, all inside the last half-hour, gave City hope of an unlikely victory which goalkeeper Joe Hart was agonisingly close to completing in injury time.
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.
"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."
Manchester United - who also went out of Europe on Thursday night - now lead the Premier League by a point with 10 games remaining.
Mancini believes the manner of his side's fightback will stand them in good stead for the weeks ahead.
He said: "If we have the same spirit as we had in the second half we can win the next game against Chelsea.
"And I am confident for the Premier League because we stayed on top for seven months and now we are in second position, one point behind. I am very confident we can win the title.
"I think that now it will be a good fight until the end of the season because we have only the Premier League and we can put all of our strength into this. I think it will be good."
Mancini joked that City followed United out of the competition to focus on their title bid.
He said: "We were envious of United because they lost, so we wanted to lose this game!"
Balotelli produced one of his more eccentric performances.
His touch in the first half was poor and frustration got the better of him at times, most notably when he argued with Mancini after conceding the free-kick which led to the Sporting opener.
Mancini said: "I was disappointed with him when he conceded the free-kick, but it is not his fault we lost this game."