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Igor Shesterkin and Adam Fox of the Rangers react after the Tampa Bay...

Igor Shesterkin and Adam Fox of the Rangers react after the Tampa Bay Lightning scored a goal during the first period at Madison Square Garden on April 7. Credit: Jim McIsaac

GREENBURGH — At their much-sooner-than-expected Breakup Day on Monday, the Rangers players glumly addressed the media one by one, trying to make sense of just how they could have missed the playoffs, one season after winning the Presidents’ Trophy and reaching the Eastern Conference finals.

“Everyone has to really look in the mirror,’’ defenseman Adam Fox said. “This year was unrecognizable as the team that’s made a conference finals in two of the past three years and has had a lot of success. And a lot of those characteristics and traits that led to that success, just . . . weren’t there this year. So, yeah, it certainly feels different. I think we’re all asking why.’’

The players knew the firing of second-year coach Peter Laviolette, who led the team to a franchise-record 55 wins and 114 points in his first season but lost his job after going 39-36-7 (85 points) this season, was not a good look for the players who make up the core of the team.

Laviolette’s predecessor, Gerard Gallant, also led the team to the Eastern Conference finals in his first season, then got fired after his second.

“It’s hard not to look at us as players and say, why is that happening?’’ Fox said. “We seem to have a lot of success [in the coach’s first season], and then, I don’t know, it turns. I don’t think us as players at any point didn’t like ‘Lavi,’ or thought his message wasn’t getting through. But it just seemed the execution of it was not there.’’

Several players acknowledged the loss of Barclay Goodrow last summer, and the offseason drama involving Jacob Trouba, and Trouba ultimately being traded to Anaheim in December, did weigh on the locker room, though no one would go so far as to say those moves were the reason why the team struggled.

“I don’t know if I would say there was some type of stress,’’ Mika Zibanejad said. “With ‘Goody’ being gone . . . and obviously the whole thing with ‘Troubs’ started . . . But then we don’t get up to the level of play that we should with this team.’’

Zibanejad’s longtime linemate and friend, Chris Kreider, diplomatically danced around the issue of his name being leaked as having been on the trade block in a memo sent by GM Chris Drury to the other 31 general managers in the league.

“That wasn’t the first time, and] it won’t be the last time that that kind of stuff comes out,’’ Kreider said. “That’s part of professional sports, unfortunately. I’m lucky I don’t have any social media, so I wasn’t really aware of it till people close to me brought [it] to my attention.”

Kreider, who called the season “challenging,’’ revealed that he battled several injuries. First there was back trouble in November, and then, after Christmas, an illness that eventually got into his inner ear and led to him getting vertigo. Then, in his first game after the NHL’s 4Nations Face-Off break, he injured his left hand in the third period of a game against Buffalo, and that injury bothered him the rest of the season and may need surgery to correct it.

As far as whether he wants to return next season, Kreider left no doubt that he does.

“This is home for me,’’ he said. “This is the organization that gave me an opportunity to live out my dream . . . I want to help, in whatever fashion, win hockey games.’’

Notes & quotes: Defenseman Braden Schneider, who missed the final two games of the season, had surgery to repair a torn labrum in his right shoulder. He said he started experiencing soreness in the shoulder two seasons ago, and the tear was discovered last season, but he was able to play through it. But the tear got bigger this season, and once the Rangers didn’t make the playoffs, he decided to have surgery. He should be good to go for training camp . . . Forward Adam Edstrom, who missed the last 31 games, also had surgery, though he wouldn’t say where, other than it was somewhere on his lower body. He has started skating and expects to be ready for camp . . . K’Andre Miller and Will Cuylle said they had not heard from USA Hockey and Team Canada about playing in the World Championships . . . Zibanejad said he couldn’t confirm whether he will play for Sweden . . . Defenseman Urho Vaakanainen and center Juuso Parssinen said they have been contacted by Finland, but both said they hadn’t decided if they will play . . . J.T. Miller attended the funeral of a close friend and was not at Breakup Day.

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