Ticketless fans fought with stewards and police as they attempted to break through the gates at Wembley stadium for the game between England and Italy on July 11.
And the FA have now announced an independent review into the security breaches will take place.
An FA statement said: "We are determined to fully understand what happened outside and then inside Wembley Stadium."
The FA has been hit with four charges by governing body Uefa concerning the behaviour of fans.
They relate to disturbances caused during the national anthems, an invasion of the pitch, the throwing of objects and the lighting of a firework.
A Uefa ethics and disciplinary inspector has also been appointed to conduct a disciplinary investigation into events involving supporters that occurred inside and around the stadium.
The FA announced last week it would be conducting a full review after a "large number of drunken yobs" tried to force their way in to Wembley without tickets.
The statement also said Baroness Casey of Blackstock has been commissioned to report on the facts and circumstances involved.
It added: "We continue to work with the relevant authorities in support of their efforts to identify those responsible and hold them to account."
Football Association chief executive Mark Bullingham apologised to fans and said the security team had "never seen anything like it".
He said the FA would be working with authorities to ban anyone who had managed to force their way in and do everything possible to prevent such an event happening again.
Images of seven men being sought in connection with the disorder have already been released by police.
England lost to Italy in a penalty shootout after the match had ended 1-1 after extra time.