The Red Wings have lost eight straight games to Montreal (0-7-1) and have been outscored 45-17 in that span.
"I have no idea why this keeps happening against that team," Blashill said. "They outcompete us on a regular basis. It is a joke."
Tatar gave the Canadiens a 1-0 lead 6:16 into the game, and Montreal put the game away with five goals in the second period.
After the Canadiens killed back-to-back Red Wings power plays, Shaw made it 2-0 at 2:22.
Gallagher made it 3-0 at 11:19 when he scored his Montreal-leading 27th goal from the right face-off dot.
The Red Wings failed to get off a shot on a 2-on-1 rush later in the period, and the Canadiens turned it into a 4-on-2 break the other way, with Domi scoring to make it 4-0 at 13:48.