Horne released a statement following Wigan's 2-0 win over Millwall at Wembley, which was marred by fighting amongst the Lions supporters. Ten fans were arrested and a full investigation, conducted by the FA and the Metropolitan Police, is now ongoing.
"The FA deplores scenes which have taken place," Horne said. "They are unacceptable and everything will be done to take action against those involved."
Horne added: "The Metropolitan Police and the FA are this evening investigating scenes of sporadic violence and disorder in the Millwall FC end at today's FA Cup Semi-Final.
"The FA and Wembley Stadium will work with police and representatives of Millwall FC to review all events. We will look to ensure those involved are identified and we would call for criminal charges and a football banning order to be brought against them."
Repeated eruptions of fighting among the Lions supporters left some fans bloodied and younger ones in tears. A Scotland Yard spokesman confirmed: "Ten people have been arrested following sporadic disorder among fans in the Millwall supporters' area at Wembley. Investigations into the circumstances of the incidents are continuing."
Wigan chairman Dave Whelan told BBC Radio Five: "I can't understand why the Millwall fans would fight each other. I understand if they want to fall out with the visiting team, but why would they fall out amongst themselves? It just gives football a very, very poor reputation.
"We know Millwall are a tough club, their team's tough to play, the supporters are Millwall Millwall Millwall... straight through. But don't fight each other. I couldn't understand that."
Millwall manager Kenny Jackett was not aware of the scuffles when quizzed soon after the full-time whistle, and he said: "I've just heard about that. I wasn't aware of any fighting during the game, not aware of any problems. I'll need to examine the facts before I can give an opinion.
"I promise you, I wasn't aware of it during the game. I am not saying it didn't happen. Until I see it, it is difficult to form an opinion. We want to be talking about football. I need to be able to form my own opinion. I am sure the evidence is there. I am not denying that."
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