Toure wants Roberto Mancini's men to set their sights on catching his former club rather than becoming obsessed with just claiming local bragging rights.
He said: "You could say that the goal against United has been the highlight of my career so far.
"It was a big moment for the club and to also score in the final against Stoke was also important because it made the fans happy. Thirty-five years is a long time to wait for a trophy.
"There are new challenges now. Against United we will be aiming to stay at the top of the league.
"My hope is that one day we will be up there with Barcelona. With the players Barca have I think that they will be the best for a while yet. But they are the club we should try to be like. We must keep improving.
"City have only just started winning trophies again, but one day I think we can start winning several trophies every season like Barca.
"City have a fantastic ambition. Just look at the players we have signed - some of the top players in the world.
"I think the owner wants to take the project to the very top - and that means Barcelona. I think the next few years will see us win trophies."