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.
"For me the only reason we have not qualified yet is because we are in the toughest group.
"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."