The blue half of Manchester clinched the league title in the final seconds of the season - ending 44 years of waiting for the club's supporters.
"The last game was a game that will remain a very strong part of our history," Kompany told CityTV.
"I think there will be people speaking about this game for 50, 100 years to come. But in the same way I have enjoyed it, I am looking forward already.
"One of the main things for me is to not keep looking back at this game for too long. I just want to move on."
City begin the defence of their trophy with a home clash against newly-promoted side Southampton on August 18.