Wigan are to carry out a full investigation into the crowd disturbances which marred the club's dramatic FA Cup victory over Manchester City on Monday.
City striker Sergio Aguero became involved in a physical exchange with a Wigan supporter as thousands of fans spilled onto the field following the final whistle at the DW Stadium.
A number of fans also headed towards the end where City supporters were sat to continue their celebrations, sparking further disorder.
Advertising hoardings were ripped out and thrown onto the field along with other objects, while missiles were also thrown from the field into the stand. There were also clashes between fans and police and stewards.
Wigan chief executive Jonathan Jackson said in a statement: "Whilst we appreciate that the vast majority of supporters who ran on to the pitch did so spontaneously to celebrate a famous victory, we were disappointed with the action of a minority of supporters who acted in an inappropriate manner.
"Player and staff safety is of paramount importance and we will conduct a full investigation."
City have not yet commented but Press Association Sport understands the club consider the events unacceptable and intend to discuss the issue with Wigan.
The Football Association is assessing the situation but is yet to say whether either club will be investigated. The report of referee Anthony Taylor and video footage are likely to be taken into account.
The governing body could also look into a confrontation between City manager Pep Guardiola and his Wigan counterpart Paul Cook. The pair exchanged heated words after City's Fabian Delph was sent off late in the first half.
Their argument continued in the tunnel after the sides left the field at half-time and television pictures showed Guardiola having to be restrained by colleagues.
Guardiola later played down that incident, suggesting he had been annoyed that Cook had left his technical area.
"Nothing happened in the tunnel, nothing happened with my colleague," the Spaniard said. "It was just please stay in your position, that's all, and then finished."
League One Wigan beat the runaway Premier League leaders 1-0 with a 79th-minute strike from Will Grigg.
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Chief Superintendent Stuart Ellison of GMP's Territorial Commander for Wigan, said: "Football is a family event and the disruption that players and fans alike faced last night will not be tolerated.
"As soon as people were on the pitch, we immediately deployed our resources to the front of the stands, where they were able to keep the two groups of supporters apart and prevent any further disruption.
"Our officers met with the club and other partners ahead of the match to carry out a full risk assessment, which ensured we had the appropriate resources for the number of people attending.
"Emotions always run high at football matches and sometimes this means that officers have to intervene to ensure the safety of the fans.
"We have made two arrests but as our investigation into last night's disruption continues, I'd ask anyone with information about the incident to please come forward."