Flames general manager Craig Button made the change after deciding the team's fortunes weren't going to improve under Hay.
"You come to a point where you have to make an assessment: Can it change?" Button said at a news conference just before the Flames played the Columbus Blue Jackets with Gilbert behind the bench. "And I came to the point where I didn't feel it was going to change."
Hay was fired at the team hotel just hours before the game. Gilbert was in his first year as an NHL assistant before being promoted.
Calgary was 23-28-13-4 and 15 points out of the final playoff spot in the Western Conference before losing 3-0 on Wednesday night.
"We've got a lot of things to work on," Gilbert said. "We competed hard, but when you make mistakes they come back to bite you."
Gilbert said the remainder of the Flames' season would be an evaluation period.
"We're just going to sit back and take a look and see what goes on from here," he said. "We know we have a lot of work to do in a lot of areas. That's our focus, on getting better. We're looking ahead."
Hay was hired Aug. 1, He replaced Brian Sutter, who was fired at the end of last season. Hay had spent the previous two seasons in junior hockey as coach and general manager of the Tri-City Americans, based in Washington state.
Hay was an assistant with the Flames during the 1995-96 season, the last year they made the playoffs.
He coached the Phoenix Coyotes to a 38-37-7 record and a playoff berth the following year, but was fired after the Coyotes were eliminated in the first round in seven games.
He later spent time as an assistant with the Anaheim Mighty Ducks.
Button notified Hay of the firing shortly before the team came to Nationwide Arena for the game with Columbus. Button said Hay disagreed with the decision.
"If you didn't disagree, a lot of things would be called into question," Button said. "Don's a good person, a good man. It's not the outcome he saw happening."
Gilbert was coach of the AHL's Worcester Ice Cats for three seasons before joining the Flames last summer. He played 15 years in the NHL with the New York Islanders, Chicago Blackhawks, New York Rangers and St. Louis Blues, winning two Stanley Cups with the Islanders and one with the Rangers.
Gilbert said he hoped the Flames would become more consistent.
"At times during the course of the year, we played like we can play with anybody in the National Hockey League," he said. "Then there's times where we've played like we don't belong in games."
Flames captain Dave Lowry said the players were behind Gilbert, just as they had been behind Hay.
"It's a tough situation for him to come in," Lowry said of Gilbert. "He'll be very professional about it. What we have to do now is move forward."
Button also added former NHL player Brian Skrudland to the coaching staff. Brad McCrimmon and Rob Cookson will be retained as assistants.
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