Uwe Rosler’s side beat City in the final of last year’s competition and poured more misery on the hosts with a 2-1 win thanks to goals from Jordi Gomez and James Perch.
Nasri did manage to get his name on the scoresheet as he pulled one back for Manuel Pellegrini’s men but it was to prove no more than a consolation for City.
Wigan will now go on to meet Arsenal in the semi-finals of the tournament, at Wembley, with Hull City taking on Sheffield United in the second semi-final.
City, meanwhile, must now regroup and face a tough fixture on Wednesday as they travel to Camp Nou to take on Barcelona in the Champions League, trailing 2-0 from the first leg.
Nasri has admitted his side were not at their best against the Latics but has urged City to focus on their trip to Spain.
“Disappointing performance from us, sorry to the fans let's focus on Wednesday and the league,” he wrote on Twitter.
Captain Vincent Kompany also gave his thoughts on the game, suggesting the team would learn from their shock defeat.
"If any lessons have to be learned, it's that anything is possible in football and that's not unimportant considering the task that's ahead," he Tweeted.City’s cup commitments also saw them slip further behind leaders Chelsea in the Premier League after the Blues thrashed Tottenham 4-0 at Stamford Bridge on Saturday.
Jose Mourinho's men are now nine points clear of Pellegrini’s men, albeit having played three games more, although the Blues boss insists City still have the advantage in the title race.