The FA is investigating after 14 arrests were made at Wembley Stadium on Saturday.
Fighting broke out among Millwall supporters and The Metropolitan Police say 12 of their fans were arrested. Two Wigan supporters were arrested but were not involved in the disorder with Millwall fans.
Speaking to Sky Sports News, Horne was quick to stress that they were already working hard to investigate.
"The scenes were deplorable - that sort of violence at a football stadium, we are not used to that and certainly not at Wembley Stadium and it was shocking and deplorable," he said.
"What we are working through now is investigating who was involved in the incident, we know there were tens of people involved in Millwall end."
Horne says that because of the amount of television footage, they were confident of catching everyone involved - but they could not comment on whether everyone involved was actually from Millwall or not.
"We have loads of footage, there is loads of camera footage and our own CCTV footage and we are working through all of that with the Metropolitan police and Millwall Football Club to understand who was specifically involved," he said.
"I know 11 arrests were made and Millwall Football Club are in constant touch with us to be as cooperative as they can and we are working very closely with the Metropolitan police and are well joined up with them, and we will work through the info in the next few days."
Horne says anyone found guilty will be hit by their own actions as well as the law.
He added: "Identifying them should be straight forward and we would like to see criminal action taken against them and also if you like football criminal action, banning orders will be entirely appropriate and Millwall particularly reiterated that."
Horne confirmed that at the moment Millwall themselves were not under investigation, saying: "These are individuals operating on an individual basis so our investigation is on individual basis."
He also insisted that Saturday's events had not impacted in any way on how they would treat Sunday's semi-final between Chelsea and Manchester City.
Horne said: "We work closely with the Metropolitan police on every event, and with local intelligence and we farm the security and policing arrangements when we know who the finalists are - those plans have been in place for two weeks and yesterday's violence did not change that."