Lucic took a penalty late in the Bruins' loss on Thursday night and made an obscene gesture toward the fans as he entered the penalty box. He then flexed his arms as if to pretend raising the Stanley Cup.
On Friday the league announced his fine, which was the most allowed under the collective bargaining agreement.
In his first public comments since the incident, Lucic called his actions "inexcusable."
"Obviously not proud of what I did there," Lucic said after the Bruins' morning skate at First Niagara Center. "Just want to apologize to our organization for embarrassing the Bruins organization.
"Also want to apologize to our fans, and also apologize to the Montreal Canadiens organization and to the Canadiens fans. I know they can get under your skin sometimes, but they are great fans. So apologies for my actions. I regret what I did."
Coach Claude Julien said he disagreed with the penalty call but added that Lucic must do a better job of controlling his emotions.