Jordan Oesterle scored Arizona's lone goal vs. the Flames, who lead the Western Conference with 64 points.
"We're playing a first-place team and we can't have four or five guys on the outside looking in," Head Coach Rick Tocchet said. "They're a skilled team, with players that go to the net. They scored on their chances … I liked some of the effort from some of the guys. Obviously, it got away from us, but it was a good trip."
The Coyotes hung with Calgary for most of the first period, and nearly took a 1-0 lead when Richard Panik hit the right post with a shot that fooled goalie Mike Smith.
"I thought we had some good chances to take the lead, but it felt like they were scoring on every chance they got," captain Oliver Ekman-Larsson said. "We talked about being hard in front of our own net and we gave them some good looks there in the middle."
Adin Hill, who grew up and honed his hockey skills in Calgary, stopped 19 of 26 shots in his first regular season NHL start in his hometown.
"Any top goalie is going to have these type of games," Tocchet said. "He struggled on some shots, but in all fairness he hadn't played in a week or 10 days. That's hard. We're going to have to get him some games."
Arizona is off Monday and will practice Tuesday before starting a challenging two-game homestand vs. San Jose and Pittsburgh. Tocchet said the silver lining of Sunday's loss is that the Coyotes learned a lesson.
"If you don't have your 'A' game, professionalism comes into play," Tocchet said. "Good angles, being smart, living for another shift. Some guys have to learn that sometimes you're not going to have your 'A' game and you're going to have to be a little more smart."
