Russia had entered the 12-team tournament as one of the favourites, with a huge weight of expectation on their shoulders from Russian President Vladimir Putin down, but proved no match for a Finnish team that won bronze at the 2010 Games.
"Inside I am absolutely empty," Russian captain Pavel Datsyuk told reporters. "The emotion we feel right now is disappointment, disappointment that we didn't live up to the hopes placed on us."
Russia got off to a fast start but the drag of playing four games in five nights appeared to take its toll. The players were unable to mount much of an offense and lost many battles along the boards against a determined Finnish team.
Ilya Kovalchuk got the army of Russian fans inside the Bolshoy Ice Dome on their feet when he opened the scoring with a one-timer from the slot that slipped in right under the crossbar eight minutes into the game.
Finland responded 87 seconds later when Juhamatti Aaltonen took a puck along the goal line before sending it under Russian goalie Semyon Varlamov's left arm.
Teemu Selanne scored after a turnover outside the Russian end, slipping a Mikael Granlund pass between Varlamov's legs with under three minutes to play in the opening period.
Finland struck again with a short-handed tally less than six minutes into the second period when Granlund scooped up a loose puck near the side of the Russian net before flicking it just inside the post with a backhand shot.
"We had nothing to lose. We were not supposed to win. They had all the pressure," Selanne, at 43 the oldest player in the men's tournament, told reporters.
"I think they were out of gas a little bit, and we tried to take advantage of that, and the game plan worked."
Finland will play top-seeded Sweden in one of Friday's two semi-finals. The game will be a rematch of the 2006 gold medal game, which Sweden won 3-2.
After missing out on the medals at the 2010 Vancouver Games, where Russia placed a disappointing sixth, Ovechkin, the poster boy of Russian ice hockey, was hoping to make amends in front of the home fans.
He got off to a flying start, scoring 87 seconds into Russia's first game of the tournament, but the scorer was unable to find the back of a net again.
The early exit from the Sochi Games, however, hardly rests solely on Ovechkin's shoulders because a Russian offense that also features snipers Evgeni Malkin and Ilya Kovalchuk were never able to get going
"It sucks, what can I say. No emotions right now," said Ovechkin. "We had a good start, scored a powerplay goal, felt pretty good.
"But we made two mistakes that cost us the game. We tried to score another one, but despite all we tried, we couldn't score."
After a mediocre preliminary round that denied Russia a bye into the quarter-finals, the team were forced to play a do-or-die qualifier on Tuesday while Finland rested.
Finland held off the early Russian charge and then took over with an up-tempo game and superb goaltending from Tuukka Rask, who stopped 37 of 38 shots and frustrated the home team for the final 52 minutes of the game.
Varlamov, who allowed three goals on 15 shots, was pulled shortly after Granlund's goal in favour of Sergei Bobrovski but it did not spark the Russian team.
"I just feel empty, disappointed and empty inside," said Bobrovski. "It's hard to say whether this is a maximal or minimal failure. Failure is failure. How can you measure it?"