The Canadiens have scored four goals through the first three games of the best-of-7 series, which the Maple Leafs lead 2-1. They'll have to find a solution quickly with Game 4 taking place again in Montreal on Tuesday (7:30 p.m. ET; NBCSN, CBC, SN, TVAS).
"I'm not frustrated," Price said. "To be honest, I believe in these guys."
On Monday, the Canadiens were outshot 27-14 through the first two periods and have Price to thank for limiting the Maple Leafs' lead to 2-1. Montreal was able to step on the gas pedal in the third period, outshooting Toronto 15-2, but couldn't find a way to beat Jack Campbell.
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Despite the outcome, Price, who finished with 27 saves, was encouraged by the Canadiens' push and believes the goals will come.
"These guys are talented guys," he said. "I see their shots in practice every day. I have no doubt in their abilities to score goals.
"It's going to come. They've been playing some pretty solid defense on their side, but we're going to find a way to get through. Their goaltender is playing well. We're going to have to find a way to make it more difficult for him."
Although Price doesn't wear a letter on his jersey, he is acknowledged to be one of the leaders on the Canadiens. Shea Weber, Montreal's captain, said the goalie's support is an indication of that.
"It's huge," Weber said. "This is the guy who gives us a chance to win every night and makes big saves, especially like he did tonight and, for that matter, every game it seems like.
"For him to step up and say something like that and say he believes in the guys, it will give them confidence, give us all confidence, to hopefully break through."
One of Price's best saves on Monday, and arguably of the season, occurred at 10:25 of the first period. Maple Leafs forward Jason Spezza was staring at an empty net after receiving a cross-slot pass from William Nylander, but Price lunged across the crease and deflected the shot away with his stick.
Asked what was going through his mind on the play, Price chuckled.
"Pure desperation, to be honest," he said.