The Metropolitan Police have confirmed 14 fans were arrested, 12 from Millwall, after numerous fights broke out in the end reserved for Lions supporters.
Four police officers received minor injuries in the trouble and Millwall are aware that the reputation they have tried to rebuild is in danger of being wrecked.
"As a club we are devastated by the scenes we saw yesterday, which are in danger of undoing much of the good work we have done to try and change the perception of the club," said a Millwall spokesman.
"We are trying to find the answers to what happened."
The spokesman could not provide a breakdown of which arrests were Millwall and which Wigan, but the two Wigan supporters were not involved in disorder with Millwall fans.
Four of the arrests were for affray, one for affray and possession of Class A drugs, one for affray and assault on police, two for public order offences, one for assault causing actual bodily harm and possession of Class A drugs, one for a racially-aggravated public order offence, one for ticket touting, one for possession of Class A drugs, one for theft and possession of offensive weapon, and one for breach of a banning order.
The police spokesman said: "A number of lines of inquiry are being pursued.
"There will be a significant post-match review and further investigation will take place to identify those responsible for committing offences."
The information is the latest stage of a combined investigation, involving the police, FA and Millwall aimed at finding out the reasons why yesterday's game attracted so much trouble.
There has already been criticism in some quarters for the evening kick-off time, which offered supporters the chance to consume an excess of alcohol.
Some Millwall supporters were seen drinking heavily in the car parks around Wembley two hours before the match was due to start.