A last-gasp Sergio Aguero winner gave City their first ever win in the competition to leave them third in the group, one point behind the Italian side who they have to travel to play on November 22.
When asked whether the match against Napoli would be the most important fixture left in the group stages, Mancini added: "Yes, 100 per cent. I think that game will be very important.
"Before this we will play the game in Villarreal and it's important we take all the points there.
"But the game in Naples will be the crucial game. I don't know for which position, but first place is open."
Mancini was visibly elated by Aguero’s goal which secured the three points, but he refused to get carried away, stressing that there was still a lot of hard work left to do in order to qualify for the knockout stages of the competition.
"It was important for us to win this game," he told reporters after the match.
"I hope this will be very important. It was important to win the first game in Champion League and now I think anything can happen in this group in terms of first place.
"At the moment Bayern Munich have seven points, Napoli five and us four. It's open for the first and second places.
"The goal came from our last chance. I think in that moment we were lucky and you need to be lucky to score in the last seconds.
"Yes, probably it would have been very difficult to qualify if we had not won. The situation would still have been open, but now this is much better."
And the Italian hopes that Aguero’s winner builds confidence ahead of the Manchester derby this weekend.
"It was important for the Champions League," he said.
"The derby will be a different game, another situation. But it's good for our confidence and it's important to go there and do well because it will be very hard."
In contrast to Mancini’s elation, Villarreal coach Juan Carlos Garrido admitted losing a match where his side were winning 1-0 thanks to Cani’s first-half goal was difficult to take and also undeserved.
"I think we have done a good match and we did deserve - if not to win - a 1-1 (draw),” he told reporters.
"I thought we had a good match in general, in all aspects, and to lose in the last minute in this way is difficult.
"Congratulations to City because they won but we thought we deserved more from this match.
"My players thought the goal was offside but it was not offside. They thought it was unfair to lose this way but we must accept it."
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