Russia president Vladimir Putin called Stanislav Cherchesov to congratulate the national team despite their World Cup elimination.
Croatia ended Russia's surprise run to the quarter-finals on home soil with a 4-3 penalty shoot-out victory sealed by Ivan Rakitic in Sochi .
Denis Cheryshev put the hosts ahead with a stunning 20-yard strike, but they required a 115th-minute header from Mario Fernandes to take the game to spot-kicks after goals from Andrej Kramaric and Domagoj Vida.
Although Russia failed to book a semi-final encounter with England, Cherchesov claimed Putin was impressed by their display.
"Our prime minister [Dmitry Medvedev] was in our changing room. Putin called me during the day and right now. He congratulated us on a very good game," he told a news conference.
"He said that what we showed on the field was great. I told him we are disappointed. But he said we should have our eyes open and make the next steps."
Cherchesov's contract with the Russian Football Union expires in August and he was unwilling to speculate on his future.
"Let's not forecast too far ahead. You see there are changes going on in the team. I won't dare forecast too far ahead," said the coach.
"We knew from the first second, I knew where we were heading. We succeeded but we have to keep going forward."
Russia's expectations were low heading into the World Cup, but Cherchesov feels their efforts have won over the public.
He added: "You may be surprised but I try to get as much information as possible in football. There was not a single national team in the World Cup that had the complete trust of their country.
"Talking about criticism, if they trusted us or not, we trusted ourselves. To beg someone to trust in you, we didn't want to do that. We can only prove our worth by working hard.
"People didn't only start trusting, but loving us. They have fallen in love with us. They know what the national team is worth. We hope we turned the situation around for the better."