TAMPA -- Carey Price fell on his sword Tuesday, and in many ways, that is what ails the Montreal Canadiens.

On one hand, it is commendable for Price to come out and take the blame for the Canadiens' six-game loss in their Eastern Conference Second Round series against the Tampa Bay Lightning because he is seen as a team leader, and that's what good leaders do.

On the other hand, it is insane.

The Canadiens were not eliminated from the Stanley Cup Playoffs because of Carey Price. It could be argued the only reason they were even in the playoffs was because of Carey Price.

"I didn't play well enough for us to win the series," Price said after the Lightning's series-clinching 4-1 victory at Amalie Arena. "I think that's basically more or less what it comes down to."

The Canadiens have bigger problems; the fact their best player thinks he's one of them might be their biggest one.

"As a team we've got to understand that Carey's the best goalie in the world but he's also human, things are going to happen out of his control sometimes and we've got to respond for him," defenseman P.K. Subban said. "Listen, Carey will always say the right things, I'm sure he's frustrated, but we need to be better around him. I don't care what Carey says, we need to be better around him and support him more. I think too many times this year he's bailed us out and that's got to change moving forward if we want to be a successful team in the regular season and the postseason.

"If we expect him to play the way he's played this year every year, it's unfair. There's going to be ups and downs, and it's tough to be at that level every single game. He's managed to do it this year, but we have to realize our job is to make his job easier, not to make it more difficult."

This is where the Canadiens' oft-repeated mantra that they are a team in transition comes into play. General manager Marc Bergevin says it every time he is asked to assess the Canadiens, and coach Michel Therrien follows suit, as he did again after the series-ending loss in Game 6.

The loss to the Lightning completes the third season of the Bergevin/Therrien regime, and considering the Canadiens were the worst team in the Eastern Conference when they took over, they might have a point. But transition in today's NHL cannot take years; it has to happen when your core pieces are in their prime.

Price will be 28 when next season starts. Top scorer Max Pacioretty is 26; Subban turns 26 on Wednesday. Those are the core pieces of the Canadiens, and they are in their prime.

"I'm going to be honest with you; tomorrow I turn 26, and the years seem to fly by," Subban said. "So I don't look at a season as a transition season, I look at a season as an opportunity to win a Cup. I can't focus on saying we need to wait a couple of years before we can contend. We need to contend now."

The list of things the Canadiens need to reach that contender status is not necessarily that long, but it's long enough. If it was to be summed up briefly, however, it would be that they need to score.

The Canadiens were the top defensive team in the NHL this season, backed largely by Price, and that became their identity. When you are facing 29 other teams once at a time during the regular season, you can get by on that. But in the playoffs, when every team takes just as much pride in its defensive play, you need something else to lean on, and the Canadiens didn't have it.

Players like Alex Galchenyuk and Brendan Gallagher, and even Pacioretty and Subban, are still on the upswing of their careers and have room to develop. But the infusion of some established offensive talent would fill a void this team had all season.

"That's the one thing you learn about the playoffs, you've got to bury your chances," Subban said. "I think individually we've all had chances to bury, and whether it's bad luck or not being sharp enough, we didn't do enough things well to finish them, to win.

"We did a lot of good things to be in the series, but to win the series you've got to finish, you've got to be great. And we weren't great."

Coming into these playoffs, most people predicted the Canadiens would go as far as Price could take them. A similar prediction, based solely on the performance of a single player, was not made of any other playoff team.

The Canadiens were potentially great because of Carey Price. They will only become great when it is no longer solely about Carey Price.