Captain Mark Giordano said Sutter's message was direct, clear and had high expectations about the acceptable way to play.
"I'm sure guys took that to heart, and we're going to move forward and hopefully we turn this right away and start gaining some momentum here because obviously the season's not as long as most seasons (56 games instead of the usual 82)," the defenseman said. "So we've got to get going here right away.
"Most guys know what Darryl's all about. I think he's a proven winner. In L.A., he had two Cups (2012, 2014). He's been to the Stanley Cup Final here in Calgary (2004). If you're not going to listen to a guy who's a proven winner like that, you shouldn't be in the game."
Sutter is 634-467-83 with 101 ties in 17 seasons as coach with the Chicago Blackhawks, San Jose Sharks, Flames and Kings.
Assistant Ryan Huska will coach Calgary when it plays at the Edmonton Oilers on Saturday (10 p.m. ET; NHLN, CBC, SN, NHL.TV) and at home against the Senators on Sunday. Sutter is expected to run practice Tuesday.
Giordano said the pressure is on for the Flames to improve their game.
"We're obviously not where we want to be, but again, our management, our ownership, that group's been steady with their message," Giordano said. "They want to win. This is obviously another indication of that. They made the change, and now it's on us players to respond."
The full picture of Sutter must include a more personal side, Lucic said. In particular, the left wing said Sutter often doesn't get the credit he deserves for the relationships and connections he establishes.
"He's a big family person," Lucic said. "He cares a lot about his players and their families. That's a side of him a lot of people don't get to see, and that's a big part of who he is."
Forward Mikael Backlund said Sutter has a clear idea how the Flames can turn things around after going 3-6-2 in their past 11 games.
"He's coming in to win," said Backlund, who was selected by Calgary in the first round (No. 24) of the 2007 NHL Draft when Sutter was general manager. "He said it's not going to be easy, it's going to be a lot of hard work. He expects us to compete hard on a daily basis. He's coming in to win, and nothing else is good enough."