What next for Russia after Euro 2016 exit?
A 1-1 draw against England in their opening game gave Russia a golden opportunity to reach the last 16, but disappointing performances against Slovakia and Wales left them with just a single point from their three fixtures.
Slutsky took over the national team from previous coach Fabio Capello in August 2015, with the 45-year-old going on to win all of his qualifiers as Russia finished runners-up in their group behind Austria.
"I would like to apologize to the Russian supporters for our performances, the fans in the stadium and watching at home on TV, they did not deserve this," he said after the Wales game.
"I take responsibility. I had enough time to find players. If we did not succeed it is truly my mistake. Someone else should take over with a big championship to come."
Russia hosts the World Cup in 2018 and this was its last competitive match until then.
Slutsky, who has been combining the national job with coaching CSKA Moscow, added: "We still qualified [for Euro 2016] so this could ultimately prove to be a positive experience.
"The players will still play in 2018 and we will try and take the positives from this experience."
The 45-year-old will now revert to his club role.
Despite Slutsky safely guiding Russia to Euro 2016, just two wins in six friendlies in the run-up to the tournament set alarm bells ringing.
Doubts over veteran center-backs Sergei Ignashevich and Vasili Berezutski and their ability to cope with the likes of Welsh star Gareth Bale, along with the omission of all-time Russian top scorer Alexander Kerzhakov, raised big questions about Slutsky's selections.
Injuries to key players also disrupted his preparations, with midfielders Alan Dzagoev, Yuri Zhirkov, and Denis Cheryshev all ruled out before the squad was picked, while Igor Denisov's withdrawal with a thigh injury meant a late call-up for Artur Yusupov.
With the World Cup on home soil only two years away, the national side is at a critical juncture. Dzagoev's return will boost the midfield, but the rest of the squad could find their places under threat.
Russia’s squad was the second-oldest at Euro 2016, with an average age of 28.83, and nine players were aged over 30. There will be calls for younger blood in the team in the run-up to the World Cup.
Whoever takes the team forward, be that Slutsky or someone new, they will have their work cut out in making sure the side is ready for 2018.