Slutsky insisted he had not seen the trouble at the final whistle – shortly after Vasili Berezutski had cancelled out Eric Dier's opener – with hundreds of Russia fans bursting through a flimsy security cordon to attack England supporters at one end of the Stade Velodrome.
He said: "I'm not really up to speed with what's going on so – we were preparing on the game – but in any case that's clearly not the best thing for football."
Pressed on the matter, he added: "I can't really comment."
Russia were handed a six-point penalty, suspended for the duration of their Euro 2016 qualifying campaign, following incidents during the game against the Czech Republic at Euro 2012.
Omnisport understands UEFA will study reports of Saturday's violence before deciding on further action, but Slutsky refused to acknowledge the sanction ever existed.
Slutsky said: "What problem did we have in the qualifying campaign? What problems were there?
"I don't remember that situation, I think you're mistaken."
Slutsky was more forthcoming about his team's on-field efforts although he admitted they were second best for long periods.
"I can thank my players because they were very much in the game right to the death and despite the pressure they were able to score even though it's always difficult at that stage of the game," he said.
"They kept on scrapping to the end and saved a result. I'd like to point out that England dominated but we were able to contain them and their dangerous forwards."