City lost 2-1 in Italy on Tuesday and now need to beat Bayern Munich and hope Villarreal at least draw against Napoli if they are to reach the next stage.
"Our target was to go into the second stage and [now] we are depending on other teams," Mancini said.
Mancini rated City's chances of progress as "70% to Napoli, 30% to us".
The Italian refused to give up all hope, but put the onus on Villarreal to field a strong side against the Italians despite the Spaniards having little but pride to play for.
"If Villarreal play a normal game they may still get a result," he said. "If they play a serious game we can still get to the second stage.
"But Napoli are the favourites and life doesn't finish if we don't get through.
"We have still got another match to play and if we don't qualify we will play in the Europa League. Everything is not finished - never say never."
City were second best in Italy, with Edinson Cavani hitting an impressive double for the home side.
The prolific striker, who has now scored four goals in five Champions League appearances this season, grabbed a near-post header in the first half before netting the winner after 48 minutes when he side-footed home Andrea Dossena's cross.
Mario Balotelli had drawn City level just before half-time when he tapped home from two yards out after David Silva's shot had been parried into his path by Morgan de Sanctis.
The Premier League leaders struggled to impose their fluent attacking game on their hosts, but Mancini insisted the scoreline flattered the Italians.
"We didn't deserve to lose this game," he added. "After our equaliser we had two more chances to go 2-1 up. It is strange that we conceded this goal after 10 minutes.
"We had other chances to score. Their keeper was fantastic and saved three or four chances, but if you lose probably you have made mistakes.Continue reading the main story Manchester City need to beat Bayern Munich to have any chance of going throughCity also need Villarreal to take at least a point from Napoli in SpainIf City draw and Napoli lose, the Italians go through because they have a better head-to-head record
"We conceded two stupid goals."
Midfielder James Milner, who impressed in City's midfield, echoed his manager's thoughts and turned his attentions to Sunday's Premier League clash with Liverpool at Anfield.
"We had more than enough chances to win the game but they are a very good team and they were good on the break," said the former Aston Villa man.
"We gave two sloppy goals away and you can't afford to do that in the Champions League.
"It's a learning curve and we have to make sure we bounce back from it. We will pick ourselves up and hope to put in a performance on Sunday."