"I think it will be the right decision if someone else is in charge of the national team," Bilyaletdinov told reporters after a meeting with officials.
Russia, who were looking to win their first Olympic title since the Unified Team prevailed at the 1992 Albertville Games, were knocked out in the quarter-finals with a 3-1 defeat by Finland.
"I was unable to complete the necessary task and our performance was the same as four years ago. I do not want to talk about the mistakes at the moment. We have analysed the situation and if a new head coach wants to look at it, I will be happy to pass on the information on."
"I do not agree that our preparations for the Olympics were bad. We had a good training camp with players from the KHL (Kontinental Hockey League) before Sochi and they were in good shape."
Bilyaletdinov took over as head coach of the Russian team in June 2011, signing a contract until the conclusion of the Sochi Olympics.
He led the team to the world championships title as Russia won all of their 10 games.
Dynamo Moscow coach Oleg Znarok, 51, has been widely tipped to replace Bilyaletdinov, with the world championships starting in Minsk on May 5.
- Sports & Recreation