Sergio Aguero finally ignited City's European campaign by with an injury-time tap-in that secured a 2-1 win over the hard-working Spaniards at the Etihad Stadium.
It had looked like being another frustrating night for Mancini's men as they searched for their first Group A win after a draw and a defeat in their two openers.
Mancini said: "I hope this goal will be very important - it was very important to win the first game in the Champions League.
"I think everything can happen in this group, for first place.
"We know we should go to Villarreal in 15 days, it will be a very important game for us.
"Villarreal are a really good team and play football very well.
"In the Champions League when you get one chance you must score, otherwise the game can go the other way.
"We had a lot of chances and I think we deserved to win the game."