Former Manchester United midfielder Darron Gibson boosted his old club's title chances by firing Everton to a 1-0 win over the Barclays Premier League leaders.
The result prolonged a dismal record at Goodison Park for City, who have now won just once in their last 14 league visits to the ground.
Despite that unimpressive statistic - and with Mancini trailing 4-1 in his head-to-head record with opposite number David Moyes prior to the game - the Italian said he still underestimated the Merseysiders.
Mancini said: "I didn't prepare well for this game. I thought it was maybe easier. I know here it is never easy, never. I acknowledge my mistake. It is important for me to know this because, like this, I can't do the same mistakes in the next game.
"The players put everything on the pitch but I made some mistakes during the last three days preparing for this game."
When asked how he made such errors, Mancini said: "We played well against Tottenham, we won the last three games in the Premier League.
"I thought Everton were without three or four important players, and maybe we did these mistakes. It can happen."