Russian supporters leapt over security cordons into the England section of the stadium, forcing fans to flee in fear.
Slutsky was quick to point out he had not seen the incident inside the stadium, so he did not want to discuss it in his post-match press conference.
The 45-year-old told reporters he was "not up to speed" with the goings on and insisted he and his side were too busy focusing on the game to realise what was unfolding in the stands. Journalists continued to press Slutsky on the matter, but he went on to say that he "really couldn't comment."
History repeating itself
This isn't the first time Russia have been involved in this type of behaviour. Back in 2012, when facing the Czech Republic in the group stages of Euro 2012, fans clashed during the match and Russia were fined over £100,000.
When this was brought up in the post-match press conference, Slutsky played down the issue and was quick to move on. The clashes have now raised questions about Russia's hosting of the next World Cup in just two years time.
One thing Slutsky was happy to talk about was the match itself. His Russian side broke English hearts with a late Vasili Berezutski equaliser, which means Group B is now wide open.
Speaking about the performance of Russia, Slutsky admitted his side were second best for the majority of the match but "thanked" his players for staying in the game until the very end. This "scrapping" until the end, as Slutsky put it, meant Russia "saved" the result. He also stated he was happy at how well his side "contained" England.
Russia face Slovakia on Wednesday knowing a win puts them in pole position to qualify from the group, despite many writing them off pre-tournament.