Jonathan Drouin scored, and Allen made 28 saves for the Canadiens.
"I thought we had our spurts in the game," Allen said. "I thought we started really well, our first 10 minutes was really solid in that first period and we had some jump. There's some things we all definitely want to improve on including myself but we didn't get the win and that was the main thing. They have elite players on that team, high end talent and whenever you have that, you've got a good chance for success."
The Maple Leafs killed off a 5-on-3 power play for 1:44 that started at 5:18 of the third period.
"We put a lot of pressure but I didn't like our pace, our intensity," Canadiens coach Dominique Ducharme said. "I think that was a difference tonight for sure. Having a 5-on-3 in the third period and trailing by one, you need to capitalize on that."
Maple Leafs defenseman Justin Holl blocked a shot from Brendan Gallagher at 7:07 to save a goal with Campbell out of position.
"Justin, to single him out, he had the game-saver there," Campbell said. "They were moving it around pretty quick, and it was pretty tiring down 5-on-3 and all of a sudden I look over and I kind of gave them a wide-open net. I've got to watch some video on that tonight, but Justin took it away and made a game-saving block. He's a heck of a player and it was great to see him make a game-changing play like that."
Drouin put the Canadiens up 1-0 at 7:22 of the first period when he took a pass from Josh Anderson on a 2-on-1 and shot past Campbell's blocker. It was Drouin's first game since taking leave from the Canadiens on April 21 due to anxiety.
"That was good, I was really happy for him," Allen said. "When I saw he was the guy who put it in the net, I couldn't tell the reaction on the bench but I'm sure everyone was elated after the hard times he's gone through over the last five or six months, getting his feet under him again, he was very deserving of that goal."