Russia's Olympic athletes flew to Vancouver with high hopes of gold medals, world records and glory for the motherland. But today they faced a chilly reception at home when the president joined in a growing chorus of criticism after the team's worst performance at the winter games since the break-up of the Soviet empire.

Dmitry Medvedev demanded the resignation of the "fat cats" who he said bore responsibility for Russia's dismal performance, which saw them finish with just three golds. Despite bold predictions from sports officials it would finish in the top three, the country came 11th, well behind hosts Canada, who scooped a record 14 golds, and trailing South Korea, China and even the tiny Netherlands.

The result is a personal embarrassment for Vladimir Putin, Russia's judo-loving black-belt prime minister. Putin is closely linked with Russia's sporting success and was instrumental in securing the 2014 Winter Olympics for Russia, to be held in the Black Sea resort of Sochi.

President Medvedev said those who trained the Russian team before the Vancouver games should "have the courage to step down" as a result of Russia's woeful medals tally. If they refused to resign "we will help them", he said bluntly.

Over the weekend Medvedev abruptly cancelled a scheduled visit to last night's closing ceremony, apparently in disgust. "We must drastically change the training of our athletes … We have been living on Soviet resources for a long time. But that is over now," Medvedev told the ruling United Russia Party.

He added: "Unprecedented investments are being made in sports in Russia. But money is not everything. We should think about changing the training methods. The new training system must focus on athletes rather than on fat cats."

Opposition politicians demanded the sacking of the sports minister, Vitaly Mutko, and Russian Olympic committee president Leonid Tyagachyev, both close allies of Putin. The pair were antiheroes, the Moskovsky Komsomolets newspaper said, ridiculing Tyagachyev's Panglossian prediction Russia would finish in the top three.

Other commentators pondered the reasons behind Russia's sporting decline. Since the 1960s the Soviet Union has performed impressively at the Winter Olympics, dominating disciplines such as ice-skating and hockey. This year Russia's ice hockey team lost in the quarter-finals, while in figure skating, the country came second to America.

Under communism, sport was a mass-participation activity, with talented youngsters identified early, dispatched to special sporting academies and given free coaching. There were also regional centres of excellence among Soviet republics, with wrestlers from the Caucasus, basketball players from Lithuania and footballers and jumpers from Ukraine.

Now sport has become a pastime for Russia's rich. "If you look at the statistics for Russia's Olympic medals you will see a reduction over the past 20 years," Tamara Moskvina, a Russian figure skating coach and former Soviet national champion, told the Guardian.. "We are harvesting the results of the dissolution of the USSR."

Moskavina said sport collapsed in Russia during the 1990s, with many sportsmen and coaches finding employment abroad or drifting into other professions. "Training facilities became obsolete or simply degraded. Other centres were left behind in newly independent Soviet republics," she said.

The Soviet speed skating rink, for example, ended up in Kazakhstan.

In recent years the situation had improved, Moskvina said, thanks to a large injection of funds from the Russian government. But this was not sufficient to compensate for the exodus of top sportsmen and qualified coaches. "In order to prepare a top-level Olympic champion you need from 10 to 20 years," she said.

Another reason for Russia's Olympic failure is that millions of roubles earmarked for preparations may have disappeared. Sergey Stepashin, chairman of Russia's accounts chamber, said he was conducting an urgent audit into what had happened to Olympic funds. "We need to carry out a thorough assessment before the Sochi games," he said.

Not all of the money appears to have gone where it was needed. Today's Moscow Times reported that Russia's luge team had to make its own equipment because of a lack of funds. Albert Demchenko, 38, who came fourth in the Olympics, said there was insufficient money for his sport, adding that when his luge broke he had to repair it himself.

At the Turin games in 2006, Russia performed respectably, finishing in the top five, with 22 medals, including eight golds. This year, in addition to three golds it scooped five silvers and seven bronzes.

Russia's Olympic committee was unavailable for comment. Putin has shrugged off suggestions that Russia faces the humiliating prospect of finishing towards the bottom of the medals table when it hosts the games in four years. "Of course we expected more from our team," Putin said, while the games were nearing their close on Friday. "But that's not cause to throw up our hands, wear a sackcloth and ashes or beat ourselves with chains."