The Canucks (38-30-11) have lost three in a row and are six points behind the Dallas Stars and Nashville Predators in the Western Conference wild card race with three games left. Vancouver is 30-15-9 since Bruce Boudreau replaced Travis Green as coach on Dec. 5.
They will be eliminated if the Vegas Golden Knights defeat the San Jose Sharks in any fashion on Sunday.
"We pushed from Dec. 5 until now, and I expect us for the next three games to keep pushing again," Boudreau said. "But we know that our ultimate goal is probably not going to be reached."
Quinn Hughes and Elias Pettersson scored, and Thatcher Demko made 26 saves for the Canucks.
Dillon Dube scored twice, and Dan Vladar made 30 saves for the Flames (49-20-10), who clinched first in the Pacific Division on Thursday and are 9-1-1 in their past 11.
"We want to keep going here and have a good feeling before the playoffs," Lindholm said. "My first year here (in 2018-19) where we clinched early, it felt like we kind of slowed down a little bit before the playoffs started and it's hard to turn it on again just like that. We've got to keep going and keep building our game and just create the good feeling before the playoffs."
Lindholm put Calgary up 1-0 at 2:44 of the second period when he caught a cross-ice pass from Johnny Gaudreau and shot over Demko's glove on the power play.
"It's obviously a good number," Lindholm said. "Coming in, you always want to improve. Thirty has been a goal and a good number to reach and obviously I got that, so just had to keep going."