City have flopped for the second consecutive season in the Champions League.
But Kompany told City's website: "I think everyone in the football world knows City are destined for greatness in the Champions League and if they don't, they would be ignoring the truth.
"We've proved as much in the Premier League and the fans have no reason to doubt that because it will come.
"There will be a City team that will go far in the Champions League, but you can't jump into the most difficult competition in the world and win it. It takes time and it's good it's been so difficult for us because we are learning quickly that you have to be ready for it and hit the ground running."