Skirmishes between English supporters, their Russian counterparts and French riot police had overshadowed the build-up to the Group B fixture, before tensions worsened after the match which ended 1-1.
Russia supporters appeared to rush England fans inside the Stade Velodrome on Saturday, forcing helpless people to try and escape by any means they could while police were absent.
These latest scenes come off the back of news that two England fans are fighting for their lives following clashes before the game.
Omnisport understands UEFA will launch a probe into the fighting inside the stadium, having been powerless to investigate incidents in Marseille during the week.
"We regret the trouble in Marseille today," an FA statement read.
"The FA is very disappointed about the terrible scenes of disorder and of course condemns such behaviour.
"It is now in the hands of the relevant authorities to identify those involved in trouble and deal with them appropriately and quickly.
"At this time the FA urges England supporters to act in a respectful manner and support England in the right way.”