Montreal plays at the Winnipeg Jets in Game 1 of the second round Wednesday (7:30 p.m. ET; NBCSN, CBC, SN, TVAS).
Despite missing the final six games against the Canadiens, Tavares said he shares the blame for the Maple Leafs coming up short in the Stanley Cup Playoffs again. Toronto, which reached the playoffs for a fifth straight season, has not won a postseason series since 2004, losing six in that span. The Maple Leafs were the No. 1 seed in the Scotia North Division this season.
"It's really hard to put into context the disappointment, just the devastation of what this loss brings to the group and the challenges we have ahead of us," he said. "It's been a tough go. I think we all take significant responsibility."
Center Auston Matthews and forward Mitchell Marner, who combined for 61 goals during the regular season, combined for one in seven playoff games against Montreal.
Tavares was third on Toronto during the regular season with 50 points (19 goals, 31 assists) in 56 games, behind Marner (67 points; 20 goals, 47 assists) and Matthews (66 points; 41 goals, 25 assists).
Tavares, who was born in the Toronto suburb of Etobicoke and grew up in nearby Oakville, Ontario, said the frustration of Maple Leafs fans in the community hits home.
"We feel like we've let our fan base down," he said. "I know how much each and every person cares and how bad we want to have success, and we won't stop trying to get better and finding our way through this."
Tavares' recovery has been swift to the point that he took part in the optional morning skate prior to Game 7 on Monday.
"I don't remember the hits," he said. "I remember the whole day, my first couple of shifts. And then I remember feeling parts of it. As I was kind of on the ice and getting put on the stretcher and getting onto the ambulance and kind of when I was getting onto the ambulance, is when I really started to kind of get the grasp of it, kind of get a better understanding of what was going on."
Tavares said Perry reached out to him after the game. He also said he has not watched a replay of the incident.
"I've never been remotely close to it, and I know how traumatic it was for my family, especially how many times they say it," he said. "So when I was talking to them at the hospital, and even the next day talking to teammates and people in the organization over the following days, just even the looks on their faces even talking about it, made me realize it was pretty significant.
"Maybe I will watch it. I'm not sure. I haven't really focused on that. I've just tried to get better."