The Latics managed to cause an upset by defeating the tournament favourites with a 2-0 victory on home soil.
The result ended City's hopes of claiming the quadruple - FA Cup, Premier League, EFL Cup and Champions League - this season, and tensions rose on the final whistle.
According to BBC Sport, advertising hoardings were thrown from the end of the stadium housing the travelling City fans.
In response to the unsavoury scenes, Wigan chairman David Sharpe told BBC Radio 5 live: "It is not nice to see, football is emotional, it is what it does to fans, but I don't like to see this at the end of the game. It is a massive result, but we have to stay classy in football, I don't like what I am seeing here."
City were forced to play 45 minutes with 10 men following Fabian Delph's sending-off.