The Bruins are 1-3 in overtime, winning 2-1 at home against the Stars on Nov. Nov. 5.
"Overtime hasn't been our friend," Cassidy said. "We don't manage the puck. We give up odd-man rushes. We don't deserve to win."
Defensemen Jakub Zboril and Connor Clifton each made his NHL debut for Boston, which played without Zdeno Chara, who injured his knee in a 6-3 loss to the Colorado Avalanche on Wednesday.
Zboril played 10:53 and blocked two shots. Clifton played 18:53, took two minor penalties and had a five-minute major for fighting Jason Spezza.
Defenseman Gavin Bayreuther, who grew up in New Hampshire as a Bruins fan, made his NHL debut for the Stars. He played 14:48, took a tripping penalty and blocked three shots.
Bruins forward Patrice Bergeron skated to the locker room at 7:45 of the second period after being hit into the boards by Radek Faksa. Bergeron returned about five minutes later, just before forward Brad Marchand took a minor penalty for slashing and then was assessed a 10-minute misconduct penalty. Marchand had 18 penalty minutes and leads the NHL with 66.
Bergeron struggled to finish the game with an upper-body injury and will be evaluated Saturday, Bruins coach Bruce Cassidy said.