The goalie was injured in a collision with Red Wings forward Dylan Larkin late in the period at Little Caesars Arena. Allen stayed in the game but was removed by the NHL concussion spotter with 48 seconds left and replaced by Sam Montembeault.
Larkin fell into Allen after a check by Canadiens defenseman Jeff Petry.
"I was worried about Jake there," Larkin said. "I'm at full speed, Petry is at full speed, and it was just a little push. I was at the end of my shift and I was tired and I just couldn't do anything to avoid it. … It was a tough play and I feel really bad about it."
Montreal led 1-0 at the time, with Allen making eight saves. Detroit scored on two of its first three shots against Montembeault for a 2-1 lead.
"Obviously, I didn't want to come into the game and give up two goals," Montembeault said. "But I couldn't let that bother me. They were on the board and there was nothing I could do about it. I just tried to keep making saves and give us a chance to come back."
Larkin tied it at 2:36 of the second period from a sharp angle, and Pius Suter gave the Red Wings the lead at 3:21.
The Canadiens lost 3-2 when Larkin scored 1:41 into overtime. Montembeault made 22 saves.
"It's a tough situation for us when Jake can't come back for the second period and then they take the lead," Montreal coach Dominique Ducharme said. "But we kept playing and I thought we had a really good third period. It's a shame we couldn't win it in overtime."
After the game, Montreal recalled goalie Cayden Primeau from Laval of the American Hockey League. The Canadiens play at the Boston Bruins on Sunday (7 p.m. ET; NESN, TSN2, RDS, NHL LIVE).
