Fans angry at Russia's lame World Cup display hurled condoms at the federation's Moscow headquarters Monday and demanded coach Fabio Capello's sacking, ITAR-TASS news agency reported.
Former England boss Capello's contract ties him to Russia until the 2018 World Cup on home soil.
Despite Russia's first-round exit the 68-year-old Italian was given a vote of confidence by the country's football supremo Nikolai Tolstykh and sports minister Vitaly Mutko.
Around a dozen fans descended on the federation, protesting against Tolstykh's pro-Capello stance, reports said.
"I think a huge amount of work has been done by our national team under Capello's guidance," Tolstykh said last week.