Allen, who made his first start in seven games, is 0-5-0 in his past five starts and hasn't won since Dec. 23.
"I felt great. It was my first start in a while but I've been working hard and I've been ready," Allen said. "I felt like myself. It wasn't enough tonight."
Krejci scored at 12:32 of the first period during a scramble in front after Jake DeBrusk's shot went off Allen and deflected up in the air. Blues defenseman Joel Edmundson tried to clear the puck out of the crease, but Krejci intercepted the puck and shot it into the empty net for a 1-0 lead.
Blues coach Mike Yeo challenged for goaltender interference, but the play was upheld after video review.
It was the first time in nine games the Bruins scored first.
"Even without the first goal, I thought our start was a lot better than the last eight, nine games," Bergeron said. "So, we just had to keep pushing and finding a way. And obviously, getting the goal gave us some more momentum to carry over."