Russia's first and only goal of the match came ten minutes into the first period when Pavel Datsyuk scored off a pass from Ilya Kovalchuk. Finland's first goal came via Juhamatti Aaltonen followed by two from Mikael Granlund.
"There were great hopes placed on us and we didn't live up to them," a disappointed Russia captain Datsyuk said.
"I cannot explain my feelings. Inside I am absolutely empty. The emotion we feel right now is disappointment, disappointment that we didn't live up to the hopes placed on us."
In the other match of the day, USA entered the semifinals for the second straight time after they beat the Czech Republic with a convincing 5-2 victory.
James van Riemsdyk scored the first goal for US as the Czech Republic got their first courtesy Ales Hemsky.
Dustin Brown and David Backes netted the second and third goals for the Americans, with, nearly ten minutes into the second period, Zach Parise making it 4-1. Phil Kessel got the fifth for the US , with Hemsky scoring his second consolation goal for the Czechs.
US came into the match with two days' rest, whereas the Czech Republic had to play Solvakia on Tuesday which proved to be the difference in the end.
"They had more energy. It's not an excuse, it's just the way it is," Ondrej Pavelec, Czech Republic's goaltender, told reporters.
The US camp seemed delighted to advance to the semis, with Max Pacioretty, the American forward, noting it was the way his team gelled together that really made the difference.
"Everyone on this team realizes you have to play for the team and check your ego at the door," he said. All of us are the top players on our team back home and you come here and you're asked to play different roles.
"You see everyone in the room, willing to go to the dirty areas, block shots, make hits."
USA will face Canada in the semifinals one phase short of the last Olympics, when Canada got the better of their neighbours in an epic gold medal game in Vancouver 2010.
"They're obviously the favourite coming into the tournament, and we've opened up a lot of eyes with our play, but we have more in the tank to give and to show," Pacrioretty said of the Canada encounter.
The much-awaited semifinals will be played on Thursday with Finland vs Sweden up first, followed by the three-time defending champions Canada's clash against the US.