Cooper, who signed a multiyear contract extension on March 26, became coach of the Lightning on March 25, 2013; he is the longest-tenured coach with his team in the NHL. The Tampa Bay leader in regular-season coaching wins, he is 305-159-44 during the regular season and 36-32 in the playoffs.
"If I hadn't re-signed [Cooper] when I did, I'd be looking to re-sign him now," BriseBois said. "There's no point looking for the next [Cooper] when I have the original and I like the original and I have faith in the original."
BriseBois said there will be some roster changes simply because of the Lightning's salary-cap situation. Defensemen Anton Stralman, Dan Girardi, Braydon Coburn and Jan Rutta each can become an unrestricted free agent on July 1.
"Today, it's too soon," BriseBois said. "The emotions are still too raw. I'm in no position to give you any indication as to what those changes will be."
He did say it's likely center Brayden Point, a pending restricted free agent, will sign a long-term contract with Tampa Bay.
"The story of these players, the story of this team, the story of this nucleus of players and of this coaching staff, it's not over, it's still being written," BriseBois said. "The best and most memorable chapters lie ahead.
"I don't know when, but I know that when we do it will be all the more sweet because of the disappointments that we will have experienced along our journey to making that happen, including the disappointment that we're feeling right now because of the outcome of this playoff series."