City disposed of FC Copenhagen in their two-legged last-32 tie in February and tackle Danish club Aalborg in the next round on Thursday.
And, with the likes of AC Milan no longer in the competition, Dunne has his sights set on lifting the Uefa Cup trophy.
He told the Manchester Evening News: "The longer we stay in Europe, the more our name is lingering around, and the more people will think that City are actually quite a decent side.
"We want this Uefa Cup run to continue. It's in our hands, and we feel with the draw that we've got a chance of progressing."
Ambitious and affluent side City are aiming to build as a club this campaign with further lavish spending expected this summer, and success in Europe would go some way to attracting additional high-profile players.