"I just can't take this stress any more," the 46-year-old told reporters in Belgorod after his club team Zenit Kazan lost to local side Belogorye in Saturday's Russian Cup final.
"This is purely my decision. Nobody has forced me to quit. I'll concentrate on coaching Zenit. As you can see from today's game we have plenty of room for improvement."
Belarus-born Alekno, who started his coaching career in France, was named Russia boss in 2007 but left the job after leading his team to third place at the 2008 Beijing Olympics.
He was much more successful in his second spell as Russia coach, which began in December 2010, winning both the World Cup and the World League in 2011 before achieving his greatest triumph this year in London.
It was the first Olympic gold for the Russian men's volleyball team since winning on home turf in Moscow in 1980.
"Winning the gold in London was the biggest thrill for me but it was just too much to take. I'm not ready to do it again," said Alekno.
Stress from the job was blamed for the death of Russian women's volleyball coach Sergei Ovchinnikov, who committed suicide by hanging himself in his hotel room in August, shortly after failing to lead his team to an Olympic medal in London.
Ovchinnikov, 43, was heavily criticised by local media after his team, considered leading medal contenders in London, lost in the Olympic quarter-finals to eventual winners Brazil after squandering six match points. (Reporting by Gennady Fyodorov, editing by Justin Palmer)