At the final whistle hundreds of Russian fans broke through a feeble security cordon at the southern end of the ground to attack their England counterparts who made a hasty retreat towards the exits.
Security personnel appeared powerless to prevent the trouble, while police were slow to act.
UEFA confirmed open disciplinary proceedings will be opened against the Russian Football Union after the incidents, and the governing body condemned those who indulged in the violence.
A statement read: "UEFA expresses its utter disgust for the violent clashes that occurred in the city centre of Marseille, and its serious concern for the incidents at the end of the match inside Stade Velodrome.
"This kind of behaviour is totally unacceptable and has no place in football.
"Disciplinary proceedings have been opened against the Russian Football Union (RFU) for the following events occurring inside the stadium: crowd disturbances, setting off of fireworks and throwing of missiles.
"A decision on the sanctions to be imposed will be made within the next few days, once the RFU has been able to submit written statements and evidence.
"UEFA acknowledges that there were segregation issues at Stade Velodrome and will implement corrective measures to strengthen the deployment of security personnel at stadiums, in close collaboration with local authorities."
Russia's sports minister Vitaly Mutko said on Sunday he expected a "fine from UEFA" and admitted the country's supporters had "behaved incorrectly" having earlier appeared to pin the blame squarely on the lack of security measures inside the ground.
Speaking straight after the game, he told R-Sport: "There was no clash, that has been exaggerated. In fact, everything is fine. When the match ended, there was no barrier between the fans. The British were upset, of course, but it all quickly dissolved.
"Such matches should be organised properly. It is necessary to separate the fans.
He added: "The bad thing is there were firecrackers and flares. There were no nets. One must understand these things."