WASHINGTON — Two hard-fought exhibition games against Canada showed the United States exactly what it needs to work on before the World Cup of Hockey begins this weekend.

For coach John Tortorella, it wasn’t about the post-whistle pushing and shoving or the intensity that made the tune-up games feel more like the real thing. It’s more that the U.S. has to be sharper, especially in the tournament showdown against Canada on Sept. 20.

“We’ve got some work to do,” Tortorella said after practice Monday. “I’m glad we played Canada because they are a really good team — probably the best team in the tournament right now and you’d have to say that.”

The Americans lacked offensive-zone time during a 4-2 win Friday in Columbus and a 5-2 loss Saturday in Ottawa. Canada won gold in Sochi by having the puck in the offensive zone so much that opponents got worn down and couldn’t create chances.

Tortorella acknowledged the U.S. isn’t the most skilled team in the tournament, and it did fine physically going up against Canada in bump-and-grind, testy situations. But general manager Dean Lombardi said he and his staff wanted to build the U.S. to beat the Canadians, and that means more than just beating them up.

“Obviously we’re pretty familiar with their talent level and what they bring,” U.S. goaltender Cory Schneider said. “It’s just getting that intensity, getting that playoff feel to it. I think playing against the best prepares you the best.”

The U.S. has one exhibition game left, on Tuesday against Finland, before traveling to Toronto for the World Cup. Its opening game is Saturday against Team Europe.

With Canada serving as the gold standard and two games worth of film to study, the Americans must figure out how to beat the best at their own game of puck-possession hockey. Tortorella has some ideas.

“Everybody talks about puck possession, but sometimes puck possession is you don’t have the puck, you put it into an area to get it back and I don’t think we did a good enough job there,” said Tortorella, who won the Stanley Cup in 2004 with the Tampa Bay Lightning while preaching a “safe is death” mantra. “When we did, I just think we need to be closer there. We need to support and outnumber people there also. That’s our biggest weaknesses in the two games, so we have a little bit of work to do as we go through and prepare for the start of the tournament.”

Judging from Sidney Crosby’s cross-check to the back of Kyle Palmieri and other antics, there’s already plenty of animosity built up between the U.S. and Canada going into the first best-against-best tournament since Sochi. The U.S. lost to Canada 1-0 in the semifinals, and players haven’t forgotten about that experience.

But captain Joe Pavelski cautioned about getting too worried about Canada and losing focus.

“It’s not just about beating Canada,” Pavelski said. “Obviously it’s nice if you beat them along the way. It’s about winning a tournament. We want to get to that level with this group, and it’s about going through a lot of good teams to get to that level.”