He struggled to keep his cool when confronted in the lobby of Warsaw's luxury Bristol Hotel after the shock 1-0 defeat by Greece, according to Oleg Koshelev, a journalist with Russian media outlet Gazeta.
"The fact that we didn't meet your expectations is not our problem - it's your problem," he reportedly told fans.
The honorary president of the Russian FA Vyacheslav Koloskov strongly condemned the 31-year-old.
"Such words are not worthy of the captain,' he said. 'Arshavin has never been in the position of traveling across the country to support the team at his own expense.
"The whole team should bow down to these guys. Fans come to see good football, total commitment from players and the willingness to stand up for their country.
"Instead, the captain says it's not the players' problem, but the fans' problem.
"I believe that such a captain should not be in the team."