Bergevin defended his goaltender at a news conference Monday following the Canadiens' first-round elimination from the NHL post-season by the Ottawa Senators.
"I'm not worried at all," Bergevin said. "For sure, even Carey would say there are things he can improve, that he can be better, and I'm 100 per cent behind him.
"I believe in him. We will support him and we'll help him."
Bergevin was asked repeatedly about Price after the 25-year-old spoke openly on the weekend about the pressure of playing in Montreal. He said he would no longer even go to a grocery store to avoid grilling from fans over his performances and that he sometimes felt like a "hobbit in a hole."
But he also expressed confidence that he had the talent and the mentality to win a Stanley Cup.
Some wondered if Price was suggesting he would rather to be traded to another team, but Bergevin wouldn't hear of it.
"It's normal in a market like Montreal or Toronto or Vancouver, or even Chicago or Philadelphia," Bergevin said. "Goaltending's a difficult position, very demanding. So it's normal that a young player feels pressure.
"We'll do everything we can to make sure he gets through this stage."
Then, unable to resist a joke, the first-year GM added: "Maybe I can do his groceries for him."
Price, drafted fifth overall in 2005, was having a solid season until he and the team slumped late in the 2013 campaign. While he went 21-13-4, he ended up out of the top 40 in the league with a 2.59 goals-against average and a .905 save percentage.
His woes continued in the playoffs, where he was outduelled by Ottawa's Craig Anderson until he injured a knee late in Game 4 and was replaced by Peter Budaj, who was bombed for six goals on 29 shots in the final game.
Questions about the Canadiens' size also came up during the playoffs, as the smaller Montreal forwards did little against the big, rugged Ottawa blue-line. The Canadiens scored only nine goals in five games, while conceding 20.
Bergevin acknowledged that it would be better to be bigger, but he's not ready to tear his team apart to add size and muscle. And there are not a lot of free agents available this summer who fit the mould, except perhaps New Jersey's David Clarkson who is likely to be courted by several teams.
He said the ideal way for a team to build is through drafting and developing its own players, but that takes time.
"I believe in balance," he said. "We do have a small team, but we're a fast and young team.
"You don't change the makeup of a team overnight. There are 29 other teams that want to be big, fast and strong, but that's easier said than done. Balance is very important. Character comes into play."
He mentioned Calder Trophy candidate Brendan Gallagher, one of the team's smallest forwards, who has "character that's off the charts."
When asked what the team needed most, Bergevin did not mention size, but depth. The Canadiens were caught short when top-four rearguard Alexei Emelin was injured late in the regular season and their depth was tested when four forwards went down against Ottawa.
"That's what gets you through the playoffs. and you don't bring in depth at the (trade) deadline, you've got to bring it through the draft, through your young prospects coming through," he said.
"So the mindset stays the same. I'm standing pat. I made it clear from Day One I want to make this team good for years to come, not just for one year. You always look at all the options, but depth and character and speed is what you need to reach your ultimate goal."
The Emelin injury gave a chance for six-foot-six defenceman Jarred Tinordi to show what he can do, and they have some promising blue-liners in the minors, starting with Nathan Beaulieu and Greg Pateryn.
Gallagher and third overall draft pick Alex Galchenyuk both impressed as rookie forwards.
And they have six picks in the first three rounds of this year's draft.
Bergevin did not tip his hat on what off-season moves he will make.
It is widely expected he will buy out unused defenceman Tomas Kaberle, who has one season left on his contract at US$4.2 million. But the GM said he may first try to trade Kaberle.
Decisions are still to be made on impending unrestricted free agents Michael Ryder, Colby Armstrong, Jeff Halpern, Petteri Nokelainen and Davis Drewiske. Restricted free agents are Ryan White, Yannick Weber, Michael Blunden and Gabriel Dumont.
He said no decision has been made on whether to negotiate a new deal right away with P.K. Subban, who had a standout campaign that made him a candidate for the Norris Trophy as the league's top defenceman, or wait until next season.
Subban missed the first six games of the season while working a two-year contract worth $2.85 million per season, which was considered a "bridge" deal before he signs long-term for top dollars.
"P.K. had a really good season and he earned the nomination for the Norris," said Bergevin. "But he's still a young defenceman.
"He still has a lot to learn. He's really good, but he can be even better. So it's a work in progress with him. This year, we're happy with the direction he went."
Bergevin is up for an award of his own.
The former NHL defenceman was named as one of the three finalists as general manager of the year after taking the Canadiens from last place to second in the Eastern Conference. He brought Michel Therrien back to Montreal as head coach with success and boosted the team by signing tough winger Brandon Prust, among others.
"I'd have to be a GM to get an award, I never won one as a player," he said with a laugh. "It doesn't say much about me as a player.
"But I wouldn't have this honour if it wasn't for the job Michel and the players did this year. I'm flattered because Bob Murray (Anaheim) and Ray Shero (Pittsburgh) are bright hockey people."
He declared himself "very satisfied" with Therrien and the coaching staff. He said that even when losing in the playoffs, the team always started strong, which showed the coach had them ready to compete.
The Canadiens took a step forward by making the playoffs this season, but doing it again will be another test for a team that is still in rebuilding mode.
"It will be difficult and expectations will be higher," he said. "We made progress, but next year teams will be ready for us and we'll have to be ready for them."