Montreal is 0-4-0, its worst start since losing five straight to begin the 1995-96 season, heading into a home game against the Carolina Hurricanes on Thursday (7 p.m. ET; TSN2, RDS, BSSO, ESPN+, NHL LIVE).
"They've got to fight through it," Bergevin said. "Winners find solutions, losers make excuses. You've got to find a way."
The Canadiens have scored three goals and no power-play goals in 13 opportunities, but Bergevin said he is not considering making any trades in the short term.
"I do like our team," he said. "There are some pretty good players who are not playing up to their potential, and until they do, there's nothing I'm going to do to make a change just to make a change."
Since losing the best-of-7 Stanley Cup Final to the Tampa Bay Lightning in five games last season, Montreal has lost captain Shea Weber for the season due to a variety of injuries he played through during the postseason run.
"For sure we miss 'Webby,' we can't hide that, it's a fact," Bergevin said. "There's only one Shea Weber in the NHL, and there won't be another. He's a special player, a special individual who brought a lot to the organization."
Bergevin ruled out any possibility of Weber returning this season and called his possible return beyond that as "a long shot."
The Canadiens are also without goalie Carey Price, who left the team to voluntarily take part in the NHL/NHLPA player assistance program Oct. 7, and defenseman Joel Edmundson.
"Yes, we miss those players, but we've got to find a way," Bergevin said.
The GM revealed that Edmundson's father has cancer.
"[Edmundson] was very shaken up by the fact that his father was not doing well, so I gave him a hug and I said, 'Listen, take the time you need, and family comes first,'" Bergevin said. "So I don't know when he'll be back. But he needs to take the time he has with his family."
Bergevin, who was hired as GM on May 2, 2012, is in the final season of his contract. He declined to discuss whether he had received a contract offer but said he would like to remain with the Canadiens "in a perfect world."
"I don't want to get into that," Bergevin said. "My focus since the last game in Tampa (last season) has been to improve the team on a daily basis, and I'm not thinking about that. … What's going to happen will happen, but we're going to focus on this year with our team."