Reflecting on Sunday's derby defeat, Kompany said: "As a club and a team we are making progress and this season is just the beginning.
"Credit United for the win but in years to come there could be a different story to these games.
"The competition is going to get tougher for them. The difference was not that great. I am not saying we deserved to win or anything but we had our chances in the game. We were a completely different side to the one in my first derby earlier this season.
"I think United can get used to us getting better and better and there will be some great clashes in seasons to come."