Canada trailed 1-0 after one period, but Reinhart scored 3:05 into the second period to tie the score, then Scheifele gave Canada a 2-1 lead at 3:41.
But with Scheifele in the penalty box for tripping, Ville Jarvelainen scored a power-play goal at 10:02 of the second to even the game.
In the third, Miro Aaltonen scored to put Finland ahead for good at 7:16.
Canada struggled staying out of the penalty box all game, giving Finland nine power plays, including three in the third period, all coming after Finland took its 3-2 lead. Two of Finland's three goals came on the power play.
"I think the challenge for us obviously is coming together as a team," Canada coach Steve Spott said. "It's our first game. But ultimately I think discipline is the subplot here tonight, where we have to get used to the standard of officiating and deal with our discipline a lot smarter than we did tonight."
Malcolm Subban made 19 saves in goal for Canada as Finland outshot Canada 22-15.
"I think we've got to create more offense, but that comes from staying out of the penalty box," Spott said. "That to me is going to be our challenge here. We turned over too many pucks, took penalties and that took away from our 5-on-5 ability to create offense."
Canada played the game without Jonathan Huberdeau, who sat out to serve the final game of his four-game suspension with the Saint John Sea Dogs of the Quebec Major Junior Hockey League. Canada also lost forward Brett Ritchie during the game to an upper-body injury. However, the injury is not considered serious.
Canada has one more exhibition game, Saturday against Sweden. It opens the 2013 IIHF World Junior Championship against Germany on Dec. 26.
"You want to make sure when you hit the 26th that your team is where you need it to be," Spott said. "It's a matter of getting better every day and learning what it's like to play over here and the standard [of officiating] and the type of game that these teams play."
Contact Adam Kimelman at firstname.lastname@example.org. Follow him on Twitter: @NHLAdamK