It was the first time since finishing a worst-ever eighth in 1998 in Finland that Canada didn't win a medal of some colour in the tournament.
Valerie Nichushkin scored the overtime winner at 1:35 in front of 7,617 at the Ufa Arena.
Defending champion Sweden met the U.S. for gold in a later game.
After 14 straight years of Canadians leaving the tournament with medals around their necks, "unacceptable" was the first word out of these players' mouths post-game.
"Fourth place for Canada is unacceptable," coach Steve Spott concurred. "Unfortunately that's something we're going to have to deal with and we're all going to have to answer questions too.
"Today was a tough game. I thought our players played extremely hard, but at the end of the day when you look at the big picture, the end result is unacceptable for our country."
Canada finished first in their pool with a 4-0 record only to lose to two countries they'd beaten in the preliminary round. The U.S. defeated Canada 5-1 in the semifinal.
Canada had the best 19-year-olds available to the team for this tournament because of the NHL lockout, minus a forward and a defenceman lost to injury prior to the tournament.
Russia was motivated for a medal because their country was host the tournament for the first time since 2001.
The Russians put Canada in a hole early with three goals on their first five shots. Jordan Binnington of the Owen Sound Attack made his first start of the tournament and was pulled at 7:54 for Malcolm Subban of Belleville Bulls.
The Canadians gave chase, tying the game three times to send it to extra time. They scored four power-play goals before Ritchie tied the game at 10:45 of the third.
Nail Yakupov scored twice for the host team, which also got goals from Alexander Khokhlachyov, Kirill Dyakov and Yevgeni Mozer.
Ryan Nugent-Hopkins, Jonathan Huberdeau, Mark Scheifele, Ryan Murphy and Brett Ritchie replied for Canada. Nugent-Hopkins, who plays for the NHL's Edmonton Oilers, had three assists and Murphy had two.
Russian goaltender Andrei Makarov, who plays for the Western Hockey League's Saskatoon Blades, made 40 saves for the win. Subban stopped 18 of 20 shots in relief of Binnington.
Canada was without defenceman Griffin Reinhart, who served the first of a four-game suspension given to him Friday by the International Ice Hockey Federation for high-sticking an American during the semifinal.