The Rangers slipped from a 2011-12 campaign in which they were the top regular season team in the Eastern Conference, with Tortorella recognized as a finalist for the Jack Adams Trophy as top coach.
New York this season couldn't get past the second round of the playoffs after a regular season in which they finished sixth in the East. They reached the conference final a year ago.
President and general manager Glen Sather said the Rangers won't rush into a decision on the next coach, but figure to have one in place by the time of the NHL draft.
"As far as John is concerned, I think he was a little bit shocked, but he's a gentleman and he took it really well," said Sather, stressing that there wasn't one overriding reason for the change.
Tortorella amassed a 171-115-29 record with New York in the regular season. But the Rangers went just 19-25 in post-season play during his tenure.
"I'm very appreciative of what Torts has done here," Sather said.
The 54-year-old Tortorella was hired late in the 2008-09 season by Sather, succeeding Tom Renney.
Tortorella had been employed for the previous six seasons as Tampa Bay's head coach, leading the Lightning to the Stanley Cup in 2004 and winning the Jack Adams that same year.
The Bedford, Mass., native spent several seasons as an NHL assistant coach prior to that, including turns with Buffalo, Phoenix and the Rangers.
He's posted 410 wins in 854 games behind the bench, more than any American-born coach in history.
New York battled back from a 2-0 deficit to Washington in the first round last month, but needed a third period rally and an overtime goal to avoid a sweep against Boston.
The coach was self-critical regarding the transition between the series when talking to reporters earlier this week in the final media session of the season.
"One of the things, and it falls on my shoulders, is our team's mindset going into another round," Tortorella said. "I don't think our mindset was ready to play another series and to the level you need to be at. It didn't have a playoff atmosphere.
"That's what I struggle with right now. I didn't do a good enough job in correcting and getting their mindset back to not only play at the level of a Game 7 in the first round but get ready for round 2, which is always going to be tougher."
Tortorella added to his combative reputation while on Broadway this season, clashing with reporters and offering direct criticism of his players.
Despite adding signature piece Rick Nash in an off-season trade, the Rangers were 15th in goal production this season.
Sather plans on being GM next season
Tortorella rejected any suggestion that he had differences with sniper Marian Gaborik, who was dealt at the trade deadline to Columbus. He pointedly said that young forward Carl Hagelin "stinks" on the power play when asked about the poor special teams play in the playoffs.
For the final two playoff games, Brad Richards was scratched. Richards earned the Conn Smythe as playoff most valuable player while both were with Tampa Bay.
Sather said that decision didn't surprise him, as it wasn't Tortorella.
Some things were beyond Tortorella's control. Defenceman Marc Staal had his season, and potentially career, altered by a serious eye injury.
Staal led a young defensive group, with Ryan McDonagh, Michael Del Zotto and Dan Girardi, that progressed during Tortorella's regime.
New York faces several off-season questions, including what do with Richards, who is just two years into a lengthy and lucrative deal.
Star goalie Henrik Lundqivst, meanwhile, has just one season left on his current contract and gave the impression to reporters after the Boston loss that he would be open to listening to other offers.
Despite the challenges, Sather said the team will still expect to compete for the Stanley Cup next season.
"We plan on signing Henrik to a long-term contract," said Sather regarding the goalie.
Sather, who turns 70 in September, said he plans on remaining general manager next season.
He said the club hasn't yet considered the fate of assistant coaches Mike Sullivan and Benoit Allaire.