City must beat Bayern Munich in their final Group A match on Wednesday night and hope Napoli fail to win against Villarreal to avoid elimination from the competition. The odds have been against Roberto Mancini's men since they lost in Naples a fortnight ago but Kompany insists nobody at the Etihad Stadium has given up hope.
The Belgium defender said: "We have experience in the competition. Maybe not as a club but, individually, we have enough experience in this competition. I am convinced whatever happens we still have a lot to play for in Europe and I just hope it will be in the Champions League."
He added: "For me the only reason we have not qualified yet is because we are in the toughest group."
City are currently third in the group and will finish in that position and drop into the Europa League if the results do not go in their favour.
It has been suggested Bayern, having already qualified for the last 16 as pool winners, could do City a favour by fielding a below-strength team but Kompany does not accept that.
The 25-year-old said: "I expect Bayern to put out a strong team. That is one of the characteristics of such teams - they always want to win.
"I can't imagine they would come here and want to get beaten. If they did, we would be happy about it but I would be surprised.
"But do we need a weaker team from Bayern to win? I don't think so.
"I think they are a great team but I definitely think we have still got a lot to show in this competition."
Source: PA
Source: PA