The host country fell 6-5 to Russia in Tuesday's semifinal at the world junior hockey championship, despite a four-goal burst in the third period that added drama to a game that had looked like a blowout.
"We had to be better early and we weren't," Canadian head coach Don Hay said.
Canada will not play for gold in this tournament for the first time since 2001, when the Czech Republic beat Finland in the final in Moscow while Canada settled for bronze.
Instead Russia will meet Sweden for the gold medal, while Canada faces Finland for bronze Thursday.
Sweden beat Finland 3-2 in a shootout in Tuesday's other semifinal.
The defending-champion Russians scored five times in the third period to beat Canada 5-3 in last year's final in Buffalo, N.Y. Russia now has a chance at winning back-to-back titles for the first time since 2002 and 2003.
Russian captain Evgeni Kuznetsov, a Washington Capitals prospect and the lone returning player from last year's squad, was a one-man wrecking crew with three goals and an assist.
Defencemen Nikita Nesterov and Alexander Khokhlachev and forward Nikita Kucherov also scored for the Russians. Yakupov, an NHL draft prospect who plays for the Ontario Hockey League's Sarnia Sting, had three assists.
"We didn't finish strong, but we scored six goals and we beat Canada," said Russian forward Nail Yakupov. "Russia's better than Canada."
Connolly replied for Canada early in the second period. Trailing 6-1 in the third, Dougie Hamilton, Jaden Schwartz, Brendan Gallagher and Brandon Gormley all scored for Canada in just under a five-minute span starting at 9:27.
The Canadians pressed for the equalizer in the final minutes, but couldn't get it. Ryan Strome hit the post and Connolly had a chance at his rebound with less than a minute remaining.
"I don't know how to explain it. It sucks," Connolly said. "We had chances to score goals. We were that close to tying it up, even though we didn't play that well early."
Russia needed overtime to get by the Czech Republic 2-1 in Monday's quarter-final, but it was the faster team out of the gates.
Canada had gone undefeated in four games in the preliminary round. They'd outscored their opposition 9-0 in the first period and 26-5 overall, but they were not prepared to start the game for the speed and skill of the Russians.
"We didn't get off to the start that we have been getting off to," Hay said. "We didn't do the things we normally do, and that's drive pucks down the wall and get pucks to the net.
"We didn't do a good job getting pucks to the net off the rush, we didn't do a good job of traffic. Once we started getting more pucks, traffic and people to the net, we had more success."
Canada played in the final every year from 2002 to 2011 with a 5-5 record. With the bar set so high for Canada's junior teams, the loss was crushing for this year's squad. They faced reporters with long faces and red eyes.
Canada outshot Russia 56-24 and didn't bury enough chances early in the game.
Andrei Vasilevski stopped 44 of 49 shots in Russia's net. He was replaced by Andrei Makarov after Gormley's goal at 4:17. Makarov, who plays for the Western Hockey League's Saskatoon Blades, stopped all seven shots he faced.
Wedgewood allowed four goals on 13 shots. He left the game at 8:48 of the second period when Khokhlachev crashed into the net on Kuznetsov's third goal.
"He blindsided me after that goal," Wedgewood said. "Lower back and neck just kind of gave out. Just recover here and try to get better tomorrow."
Visentin stopped eight of 10 shots in relief.
The Canadians lost their cool after Wedgewood left the game in the second period. Russia scored their fifth goal and second on the power play when Gallagher took a high-sticking penalty on Mikael Naumenkov.
Boone Jenner was given a game misconduct for spearing later in the period and Jonathan Huberdeau took a misconduct for slashing with just under two minutes two go.
The Canadians stayed out of the penalty box in the third period and scored two of their four goals with a man advantage.
They had the Russians scrambling to hold them off in the third, but the visitors had done enough work early to get the win.
Canada now plays for bronze, a colour it traditionally doesn't get too excited about.
"Every game you play is worth playing for," Hay said. "It's an honour to win a medal at this competition, no matter what medal it is. Our guys respect the fans, respect each other and I expect them to play hard for each other."