SOCHI, Russia — As Canada’s players leapt into each other’s arms, Team USA’s players fell into each other’s arms. And as the giddy Canadians hugged, the gutted Americans huddled around their leader, Julie Chu, a veteran of four Olympics now.

And three silver medals.

“There’s nothing to be ashamed of today,” Chu said she told them. “Be proud of the way we played. Be proud of the team we are.”

Proud? Absolutely. But devastated, too.

Less than four minutes from ending Canada’s stranglehold on gold in women’s hockey, Team USA let a two-goal lead slip away, and lost 3-2 in overtime on Marie-Philip Poulin’s golden goal, her second of the game. It was Canada’s fourth straight gold medal.

“We trained our whole lives to win a gold medal here,” Buffalo Grove’s Megan Bozek said. “We didn’t train for a silver. We trained for a gold.”

And they were agonizingly close. Had they just held on to a 2-0 lead in the final minutes of the third period. Had Kelli Stack’s 150-foot shot at an empty net been an inch to the right and not thunked off the post, moments before Poulin tied it up. Had a seemingly harmless goalie pad tap by Jocelyne Lamoureux not been called a slash, negating an entire U.S. power play in overtime.

It was that close.

After the U.S. won four straight in a pre-Olympics exhibition series, and after Canada won two one-goal thrillers in Sochi, this much is clear: While the gap between North America and the rest of the world is massive, the gap between Canada and the U.S. is non-existent.

Led by goals by Megan Duggan and Alex Carpenter, the Americans led 2-0 late in the third. In fact, they outright dominated for most of the first 55 minutes.

“Fifty-five of 60, though,” said star forward Hilary Knight. “It’s heartbreaking. You go four years, and you think you’ve got the game in the bag, and something happens.”

Something like a goal by Brianne Jenner with 3:26 to play. Something like Stack’s oh-so-close empty-net attempt. Something like Poulin reprising her starring role from the 2010 gold-medal game, when she scored both goals in a 2-0 win over the U.S.

It was a thrilling game. One that can only boost women’s hockey’s profile and one that, someday, the Americans involved will be able to remember with the pride Chu talked about.

But after this one, it’ll take time to get there.

“It hurts,” said Palos Heights’ Kendall Coyne, her eyes red and her chin quivering. “It’s tough to swallow right now. But I think when we go back in the [locker] room and we sit down with the family that we have here, it’ll make everything better.”

Twitter: @marklazerus