"We were together, you were our 12th, 13th, 14th, 15th and 16th players. We wanted to advance further but we couldn't. In four years in Qatar, we'll do better, but it will be more difficult without you. So go there, everyone," Cherchesov said at the team's meeting with supporters at the FIFA Fan Fest at Vorobyovy Gory in Moscow.
Russia managed to reach the World Cup quarter-finals for the first time since the Soviet era, showing their best result at a FIFA World Cup so far.
The hosts suffered a 4-3 defeat on penalties to Croatia on Saturday after drawing 2-2 after extra time in their quarter-final and were eliminated from the home tournament.
The 2018 FIFA World Cup kicked off on June 14 and will continue until July 15, with the final set to be played at Moscow's Luzhniki Stadium.