The 28-year-old goalkeeper gifted Lee Keun-Ho the opening goal in Tuesday night's Group H encounter between the pair, but Russia hit back to salvage a point.
"I want to apologise," Akinfeev is quoted as saying by Soccerway. "It was a ridiculous goal. Any normal person should apologise and blame themselves for this moment.
"The goalkeeper of the national team should not give away such goals. The coach and the players have supported me."
Russia are back in action on Sunday when they take on Belgium.