Sergio Aguero clashed with one supporter amid the celebrations, with video footage of the incident appearing to show the City striker shove the fan after being approached.
Aguero subsequently had to be restrained from confronting the fan in question by Wigan defender Chey Dunkley.
Once both sets of players had left the pitch the clashes spread to the stands, where objects were thrown between City’s travelling support and a group of Wigan fans.
It is understood that City will seek talks with Wigan in the coming days to establish how the safety of their players was allowed to be jeopardised.
After the final whistle, Guardiola insisted he had not seen Aguero’s clash with the supporter, while Wigan manager Paul Cook stressed the importance of players being kept safe.
“Not right, not correct,” he said. “I haven’t seen these incidents and would rather not comment. With all due respect, player safety is paramount.”
David Sharpe, Wigan’s chairman, condemned the pitch invasion and the scuffles. “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,” he said.
“It is a massive result, but we have to stay classy in football, I don't like what I am seeing here.”
The evening’s ill-tempered end followed scuffles between the two managers themselves at half-time.
Guardiola and Cook clashed over referee Anthony Taylor’s decision to show a red card to Fabian Delph at the end of the first half and continued their argument in the tunnel.
It was otherwise a night to savour for Wigan, who earned their third famous FA Cup win over City in succession when Will Grigg scored 11 minutes from time.
The League One promotion contenders held out for a famous victory, one to rival their triumph over City in the 2013 final, though the post-match clashes are likely to dominate the fallout.
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