Edinson Cavani struck both goals for the hosts either side of a Mario Balotelli equaliser on another tough European night for the Barclays Premier League leaders.
Mancini said: "I am disappointed about the result and I am sorry for the lads. I think we lost undeservedly.
"We played a very good match and we conceded two goals we shouldn't have done.
"There is nothing to explain, we are a strong team and we always play well, we always play to win.
"But occasionally you can lose matches, especially in the Champions League. I am not too disappointed. We have still got another match to play and if we don't qualify we will play Europa League.
"Our target was to go into the second stage and at this moment we are depending on other teams.
"But in football anything can happen. If Villarreal play a serious match they can get a result.
"It is important we play our game against Bayern Munich."