City lifted themselves above the Italians into second place in Group A with a convincing 3-0 win over injury-ravaged Villarreal at El Madrigal.
Their hopes of progress were already likely to hinge on their trip to Naples later this month but now they have a two-point advantage over the Italians, victory will make certain.
"I think this win is important because now we have a good chance," Mancini said. "We know that everything will be in Naples.
"I think it will be an incredible atmosphere. There will be 70,000 people at the stadium. "I think it is very difficult to play but it is important to go there with this result.
Mancini said that City's feat at Villarreal became easier once they scored the first goal, by Yaya Toure went in.
Toure added the third for City after a Mario Balotelli penalty put the visitors in the clear.
City needed to be patient as Villarreal looked to press them early on but once Toure had opened the scoring after 30 minutes, the result was rarely in doubt.
"Villarreal were missing four or five important players but it is always difficult to win away in the Champions League," Mancini said.
"We had 65 per cent of ball possession, we scored three goals. I think this was important for our confidence. I think we have improved, not just in the Champions League.
"It is important for us to go in the second stage, then everything can happen with us because we are a good team. We can improve a lot in the next month."
One possible worry was the sight of David Silva leaving the field clutching his back in the second half but Mancini was not concerned.
"I don't think this is serious," he said. "He took a knock on his back.
"Also we play again in 60 hours against QPR. I think he can recover well."
Mancini's only other moment of discomfort was when he leapt up and banged his head on the roof of the dugout. He returned after half-time holding an ice pack.
"I took a knock - the bench here is very dangerous!"
The result left Villarreal bottom of the group without a point and ended their mathematical chances of progressing.
The Yellow Submarine, who have endured a miserable start to their domestic season, were without a host of key players and were well beaten by the final whistle.
"It was a very difficult game," their under-pressure coach, Juan Carlos Garrido, said.
"I want to congratulate the winners tonight. We all know this is a very hard competition.
"But tonight, despite all our injuries, we never complained and I want to congratulate our players as well. They played very well despite the 3-0 score line.
"This is the spirit of the team and I want to emphasise this. If we can go on with this feeling when we have these players back we will have better results."