But something he said about the transition period the Canadiens find themselves in may have provided a big hint as to what Bergevin has in mind for this summer.
"Eventually with teams, a change happens," Bergevin said. "I'm not saying we're disappointed with our veterans, but it's nice to see that your young veterans are taking an important role in the leadership of the team."
Bergevin addressed the media Monday to assess the Canadiens' season, one in which they finished third in the Atlantic Division with 100 points and surprised many by reaching the Eastern Conference Final before being eliminated in six games by the New York Rangers on Thursday.
The Canadiens have a number of older veterans eligible for unrestricted free agency, including captain Brian Gionta (35 years old), and defensemen Andrei Markov (35), Francis Bouillon (38), Mike Weaver (36) and Douglas Murray (34).
At the same time, several members of the Canadiens' younger core are coming of age, players like goaltender Carey Price (26), defensemen P.K. Subban (25), Alexei Emelin (28) and Josh Gorges (29), and forwards Max Pacioretty (25) and Lars Eller (24).
"Those young players aren't old, but they're not young anymore," Bergevin said. "What they've learned, the way they played in the playoffs, for me the leadership of the team is slowly changing hands toward those players. That's very important for the future of the team."
When asked if that transition could impact how he approaches his team's free agents, Bergevin said, "Possibly, yes."
Two of the Canadiens' most important leaders are Gionta and Markov, who serves as Montreal's alternate captain and is its longest tenured player.
As captain, Gionta's role on the ice is buttressed by what he does off it, serving as a respected voice in the Canadiens dressing room. However, Gionta's on-ice role this season was greatly diminished once Bergevin acquired Thomas Vanek at the NHL Trade Deadline, a move that resulted in Gionta being bounced out of Montreal's top-six forward group for the first time since he signed with the Canadiens as a free agent in 2009.
Vanek, an unrestricted free agent himself who has declared he will test the market July 1, will probably not be back with the Canadiens, but that doesn't necessarily mean Gionta will get back his top-six role, especially with young forwards Brendan Gallagher, 22, and Alex Galchenyuk, 20, pushing for more ice time. Eller, who can become a restricted free agent July 1, also proved that he is ready for more responsibility by leading Canadiens forwards in scoring with 13 points in 17 games in the Stanley Cup Playoffs.
Bergevin acknowledged Gionta's strength as a leader Monday, but then went on to vaunt the leadership qualities of other players on the team, even though no one asked him.
"We'll see what we can do with [Gionta], but he's an important part of this team," Bergevin said. "Also, I'd like to mention that we have a lot of leaders that are quiet leaders that everyday people might not notice. A guy like [Tomas] Plekanec, he might not be a player that talks a lot, but by his play, the way he competes, what he does on the ice, quietly he's a very good leader.
"Josh Gorges is a very good leader that's part of the group. I think Carey's taking that role, P.K.'s taking that role, [Pacioretty] is taking that role. I think we have a lot of young leaders on this team that will help moving forward."
Markov is similar to Plekanec in that he is seen as a quiet leader who lets his play do the talking. But unlike Gionta, Markov played a significant role with the Canadiens this season and would be far more difficult to replace on the ice than the Montreal captain.
Markov was second only to Subban with an average ice time of 25:59 per game in the playoffs. After being held off the score sheet in Montreal's first-round sweep of the Tampa Bay Lightning, Markov had one goal and nine assists in his final 13 games of the postseason.
He remains an effective player at his age, but signing Markov to a long-term deal at this stage of his career is a risky proposition, particularly due to his history of knee injuries.
The Canadiens have three young defensemen who appear ready to make the jump to the NHL next season, Nathan Beaulieu, Jarred Tinordi and Greg Pateryn. Tinordi, 22, and Beaulieu, 21, were first-round draft picks in 2010 and 2011, respectively, but neither had much of a chance to play in Montreal in the regular season largely because Bergevin re-signed Bouillon and signed Murray as a free agent last August.
Bergevin then added Weaver in a trade with the Florida Panthers right before the deadline, making for a crowded bunch seeking time on Montreal's third defense pair.
With Bouillon, Markov, Murray and Weaver all heading toward unrestricted free agency, Bergevin has to decide just how ready his trio of young defensemen is and whether he is willing to go into a season banking on so much raw talent on the back end.
Bergevin noted he doesn't need to make that determination immediately, but he will soon.
"You don't want a young kid playing once every two weeks. It doesn't serve him well; it doesn't help him for his future. If we feel as a group whatever player we're talking about isn't ready to play every day or is close to it, then he's better suited to go back [to the American Hockey League] and learn," Bergevin said. "These three players are really moving forward. It's always them that make the decisions for us. By watching them, the way they perform, you know if they're ready or not."
Then there's Subban, Bergevin's most complicated offseason project.
Bergevin was widely complimented for the way he handled Subban's soon-to-expire contract, a two-year deal worth $5.75 million he signed five games into the 2012-13 season, missing one more game after signing before finally suiting up for the Canadiens in their seventh game of the lockout-shortened season.
Since then, Subban won the Norris Trophy in 2013 and led the Canadiens in scoring in these playoffs with 14 points in 17 games.
Subban was after a long-term commitment from the Canadiens two years ago and didn't get it. Now it might be Bergevin looking for a long-term deal, and it remains to be seen whether he gets it.
Subban is two years away from being eligible for unrestricted free agency, and it's possible he will want a contract that bridges the gap to that potentially lucrative time, just as Bergevin wanted a bridge contract the last time.
Subban and Eller had a combined salary-cap charge of $4.2 million this season, a number that could potentially triple next season. Gionta and Markov alone had a combined cap charge of $10.75 million this season, money that would easily absorb the raises due to Subban and Eller and leave Bergevin some wiggle room to fill out his roster, perhaps by re-signing Markov or Gionta.
Though Bergevin would not get into details on Subban, he did list him among the group of young leaders he hopes will take over the team in the near future. But in order for that to happen he will need to get his top defenseman signed to a contract.
"By age he's still a young defenseman, but since I've been here he's taken huge steps forward," Bergevin said. "So everything with P.K. has matured, his game, the way he handles himself. We're really pleased with him. He's a big part of this team moving forward."
Bergevin came to the Canadiens in 2012 from the Chicago Blackhawks, where he served as assistant general manager under Stan Bowman as the nucleus for that perennial contender was being built.
He watched as players like Jonathan Toews, Patrick Kane, Duncan Keith and Brent Seabrook grew together and eventually took ownership of the Blackhawks, players who were drafted and developed by the team to lead it to greatness.
Bergevin wants the same thing for the Canadiens, with their own young veteran leaders taking ownership of the team to lead it among the elite.
Despite their appearance in the Eastern Conference Final, Bergevin knows the Canadiens are not there yet.
"I feel we're not a mature team," he said. "We're a good, young team. Our core is still young veterans. We're moving forward. There are teams, I look around the League, they're more mature. For them, you could almost say every year it's a guaranteed playoff team. We're not there yet. Next year we go back to the same starting line with everybody else. Our first goal will be to make the playoffs, and once you're in, everything's possible.
"Hopefully years down the road we'll be a more mature team, but we're not there yet. But we have a lot of good things going for us."
This summer, we should find out just how good Bergevin believes those things are. If he resists the temptation to bring in veterans to help support his young core, if he turns the ownership of the team over to them, it may be a sign Bergevin feels the Canadiens are closer than he's letting on to crossing that final hurdle toward elite status.