The Citizens crashed to a shock 2-1 defeat to Russian side CSKA Moscow on Tuesday, leaving them bottom of the group on just two points, with tough fixtures against Bayern Munich and AS Roma to come.
Despite being in a precarious position, club captain Kompany says he has not given up just yet.
"I am the captain and if no-one else believes any more, I am the one who believes we might just have a chance,” he said. “We do have a chance.
"There are internationals between now and our next game in the Champions League. That gives us some time to clear our heads, come back, and see how much we still have to play for. That is what we have to look at."
City have endured a tough time in Europe’s elite club competition in recent years, yet Kompany explains that this boils down to their relative inexperience in the tournament, having only made their debut in 2011.
"Let's put things into perspective - we are not a club that has been there for 20-odd years,” said the Belgian centre-back.
"We are trying to put down milestones every year and so far we have been quite successful at that. You don't just go from never playing in the Champions League to winning it. There is a process.
"Everyone will jump on the bandwagon, but I am going to go the other way and say I still believe in my team, and still back everyone at this club 100 per cent to turn it around.
"But personality will have to show in the next games, otherwise we will have to wait another year, and no-one at this club wants that."
City host Bayern on 26 November before travelling to the Italian capital to take on Roma in their final group fixture on December 10.