Police have arrested 10 people after repeated outbreaks of fighting among Millwall fans at Wembley Stadium during the club's 2-0 FA Cup semi-final defeat by Wigan Athletic.
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Some supporters were left bloodied while younger fans were left in tears.
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Millwall FC said it could not "allow the actions of a mindless minority" to undermine efforts made to lose the club's reputation for hooliganism.
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The Football Association said it deplored the "unacceptable" scenes.
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The BBC's chief football writer Phil McNulty said the violence - the first significant trouble at the new Wembley since it opened in 2007 - took place in the closing stages in several areas of Millwall's allocated end.
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He said it was a shameful day for Millwall, whose fans made up about 32,000 of the crowd of 62,335, as an increasingly tense atmosphere built up throughout the second half before trouble flared.
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Police and stewards moved in to try to stem the violence - witnessed by millions on TV - but it took some time to restore a measure of control.
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'Very sorry'
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Millwall chief executive Andy Ambler said in a statement: "Our position is clear - anyone associated with our club found guilty of violent behaviour will be banned indefinitely from Millwall matches in addition to any punishment they receive from the authorities."
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He added: "At this stage we are still in the process of establishing the full details of what happened in a section of the ground during the second half.
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"When we have those facts at our disposal and the police have completed their investigations we may be in a position to comment further."
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Millwall manager Kenny Jackett, meanwhile, said he had not been aware of "any fighting".
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"I promise you, I wasn't aware of it during the game," he said in a post-match interview.
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Told that children were carried crying out of the stadium, he said: "I am very sorry if that is the case."
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And club captain Danny Shittu said it was "sad to hear about these things happening on a day like today.
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"Things like that shouldn't be going on -it should be a great day for both sides."
Millwall fans disappointed themeselves and their club with the attitude they put up after the game. It made no sense