"You have to give your team a chance to win," said Kiprusoff, the NHL leader with 39 victories. "I didn't do that today."
Kiprusoff stopped 15 of 20 shots and lost on the road for the first time in seven starts. The Flames never led as they lost for the third time in five games to a Southeast Division opponent that's out of the Eastern Conference playoff race.
Despite holding the third spot in the West with 84 points, Calgary allowed the Thrashers to earn consecutive victories in regulation for the first time since Jan. 20.
"Kiprusoff has had better games, there's no question," Flames coach Mike Keenan said. "He would be the first to say it. We have to respond to those situations. I felt we spent too much time in the penalty box."
Kovalchuk, who has 25 goals and 14 assists in his last 29 games, made it 4-2 with a hard wrister from the right circle near the midway point of the third.
Iginla had gotten the Flames within a goal with a tap-in past Lehtonen.
"Determination has to be from the start," Iginla said. "The Thrashers were hungry tonight, and we were not competitive enough to create enough chances. We know we have to be more determined. I know I have to be better early. I don't think the last few games we have been aggressive."
The Flames were without David Moss after their fourth-leading goal scorer left before the game to attend a family funeral. Calgary dropped to 1-2 since acquiring Olli Jokinen in a trade Wednesday with Phoenix.
Little opened the scoring at 4:40 of the first with a wrister from the left side of the crease. He added his 28th goal on a power play with 9:22 remaining in the third.
Atlanta never trailed after Enstrom's third goal, a slap shot between the blue line and the circles with 2:49 left into the first, made it 2-1.
With a day off before the Flames visit New Jersey on Tuesday night, Keenan has yet to decide if Kiprusoff will start against the Devils. No. 2 goalie Curtis McElhinney dropped to 0-5-1 in a 6-1 loss Friday night at Carolina.
"Hopefully I'll be better next game," Kiprusoff said. "It's tough, but it's one loss and we can't keep worrying about it. We have to have more energy from the start. I didn't do it tonight."
The Flames were facing an Atlanta team that's building some confidence despite the NHL's lowest points total at home (28) and third-fewest overall (56). Lehtonen stopped 27 of 29 shots to win his second straight start.
"I think we want to prove to ourselves that we can play against and beat teams like Calgary and the better teams in the league," Little said. "We're winning these games for us and our fans."
Jokinen matched Calgary D Dion Phaneuf with a game-high five shots on goal. ... The Flames, who moved from Atlanta to Alberta in 1980, are 0-5-1 at Philips Arena. ... Calgary committed a season-high 13 penalties, the team's most since it killed five of nine in a 6-1 loss at San Jose on Nov. 13.