Medvedev said the poor showing was the result of a lack of Soviet spirit.
"For a long time we have benefitted from Soviet achievements, at some point they ran out. We have lost the Soviet sports school, it is simply gone, but we have not formed our own system," he said.
Russians had their hopes crushed when their ice hockey team lost in the quarter finals and Viktor Plushenko, their figure skating hero, came second to an American.
"It's very upsetting, especially as our patriotism has been linked to sporting achievements," Olga, a sports fan who works for a Moscow marketing organisation, said.
The result was especially embarrassing because the country is due to host the next Winter Olympics in 2014 at the Black Sea resort city of Sochi.
A number of opposition politicians have called for the sports minister and the head of Russia's Olympic Committee to resign.
A sections of the media has also raised doubts about Russia's preparedness to stage the Sochi games.
"In order to avoid a national disgrace, you could relocate the Olympic Games to another country," wrote one analyst in Vremya Novostei, a daily newspaper.
But Vladimir Putin, Russia's prime minister, has urged people to be at ease.
"Of course we expected more from our team…but that's not cause to throw up our hands, wear a sackcloth and ashes or beat ourselves with chains", Putin said.