"I think after a tournament like this, you need someone else to take charge of the national side at major tournaments," a despondent Slutski told journalists after his side's 3-0 defeat by Wales in their final Group B match.
The crushing loss leaves Russia bottom of the group with only one point -- a draw against England before defeats by Slovakia and Wales -- in a tournament also disfigured by violence from some Russian fans.
"First, we need to change the head coach," Slutski continued, when asked how Russia can prepare for the 2018 World Cup on home soil after the disappointment of Euro 2016.
"I have to take full responsibility. I had time to prepare and find players and if we weren't able to succeed, it's definitely my mistake."
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Slutski, who is also head coach of Russian champions CSKA Moscow, replaced Fabio Capello in August 2015 and salvaged Russia's Euro 2016 qualifying campaign but his team have been one of the biggest disappointments of the tournament.
(Editing by Ian Chadband)
