Zamula, playing his 28th NHL game, made it 1-0 at 1:45 of the first. A loose puck rolled back to the defenseman at the point, and his wrist shot beat Demko.
The Flyers outshot the Canucks 22-3 in the second period.
"We've got some guys, they better pick it up," Tocchet said. "I don't like the word soft, but I didn't see guys competing at all. And that's alarming. But saying that, we win two games, let's not get too high, it was a bad effort, so let's not get too low. But we've obviously got to go to the drawing board with some guys.
"We were off all over. We were off every single system part of it. And then the compete wasn't there. They competed and we didn't. Bottom line."
The Canucks appeared to score at 3:26 of the third period, but the goal was overturned after a replay review showed Conor Garland interfered with Hart.
Vancouver had eight shots on goal in the final 16:34 of the third.
"That wasn't up to our standard," Canucks forward J.T. Miller said. "We didn't win enough battles, not strong on the puck, not sticking to the criteria of what makes our team good. We just got away from our game. Not how we want to play."
NOTES: Couturier's penalty-shot goal was the first by the Flyers since Jakub Voracek on Oct. 29, 2016. They had been 0-for-10 since then. ... Couturier's penalty-shot attempt was the seventh in the NHL this season, tied for the most through the first eight days of any season in NHL history (2005-06, 2013-14). ... The Flyers are 4-0-1 in their past five home openers. ... Defenseman Carson Soucy had one shot on goal in 15:53 of ice time in his Canucks debut. He missed the first two games of the season because of an undisclosed injury.