The Championship strugglers booked their place in the last eight of the competition on Saturday with a 3-1 win at MK Dons.
They will now face the Premier League champions at the Etihad Stadium.
"We are going to the champions of this country and I will be proud to take my players to that stadium," Flitcroft told Sky Sports News.
"The lads have deserved this and we will make sure they go there and enjoy the day and the experience, but we want to go there and give a good account of ourselves and try and cause a cup upset.
"I hope we will give a great account of ourselves and I am really excited to lead the club on this occasion."
Flitcroft's brother Garry played for Manchester City between 1991 and 1996.