Christopher Tanev scored 34 seconds into overtime to give the Canucks the win.
"We got a point out of it. It's still frustrating," Elliott said. "We always talk about, in overtime, that you've got to make that one big save to go the other way. It didn't happen tonight.
"That's frustrating personally. We did get that point and we were seven seconds away from not getting anything from out of here.
"You have to take the positive."
Alexander Edler, channeling his inner-Kenan Thompson, launched a knuckle-puck from centre ice that beat Elliott on Vancouver's first shot of the game to stake the Canucks to a 1-0 lead at 12:44.
"Probably a five-foot sinker curveball," Elliott said.
"Not one that you want to give up but you can't really get hung up on it. You've got to move on from it. I thought we did that as a team pretty well.
"You move on and get that next opportunity to make a save. It was a good battle tonight. That goal, obviously not one we want to give up, but we did a great job sticking to our game plan and took 59 minutes and whatever seconds to tie it up.
"We did a good job doing that and sticking with what was working."
Elliott kept the Flames within one early into the second period, going post-to-post to deny Jannik Hansen's one-timer on a cross-crease feed from Daniel Sedin just 2:44 in.
A key save at a key time in the game.
"I really liked the way Ells rebounded. The save on the power play in the second could've ended our night," Gulutzan said. "To come across in the splits there and make that save equalized any shot from the red line.
"I thought our team on the bench responded well. We had a lot of energy, a lot of intensity on the bench. Maybe too much in the second period, but I'd rather tame that down than try to find it."
Miller stopped Sean Monahan, who is one goal away from becoming the youngest player in franchise history to reach 100 goals, with 3:54 remaining.
It was one of 18 shots by the Flames in the period as they pushed for the equalizer Giordano found.
"We were intense," Gulutzan said. "I thought there was a bit of a playoff atmosphere out there - a lot of stuff going on behind the scenes that maybe regulars watching the game didn't see.
"It was a hard-fought game."
NOTES: Defenseman Matt Bartkowski, who signed a two-year, two-way contract with Calgary on Thursday, made his Flames debut against Vancouver. Bartkowski, who had six goals and 18 points in 80 games with the Canucks in 2015-16, played 10:55. Troy Brouwerled the Flames with six hits. Mark Giordano played a team-high 25:23. TJ Brodie followed him at 25:07. Forwards Alex Chiasson and Garnet Hathaway and defenseman Jyrki Jokipakka were scratched for Calgary.
UP NEXT: The Flames meet the Nashville Predators at Bridgestone Arena on Tuesday (6 p.m. MT; SN1, SNP, NHL.TV).