Braden Holtby gives up a goal to Tampa Bay’s Matt Carle in the shootout. (Toni L. Sandys/The Washington Post)

After years of equating the end to abrupt, heart-wrenching postseason exits, the Washington Capitals experienced the anguish of a slow, predetermined demise over the past four days.

Eliminated from contention in the Stanley Cup playoffs Wednesday after falling too far behind wild-card teams Detroit and Columbus, the Capitals officially concluded their 2013-14 season in a fittingly anticlimactic manner Sunday afternoon in a 1-0 shootout loss to the Tampa Bay Lightning at Verizon Center.

Matt Carle scored the lone goal in the tiebreak as Washington set an NHL season record for most shootouts (21) and a new season low for itself in shots (seven) through the first 40 minutes. But while the contest mattered for the Lightning, which secured home-ice advantage in the first round of the playoffs, it will be little more than a footnote for the Capitals.

As Washington missed the postseason for the first time since the 2006-07 season, speculation is swirling around the job security of those who set the tone for the organization.

General Manager George McPhee’s contract expires this season, and in his 17 seasons the Capitals have advanced past the second round of the playoffs only once — his first season in 1997-98. Coach Adam Oates has one year left on his current contract but oversaw the team’s slide this season, during which the Capitals couldn’t stem chronic problems ranging from rapidly allowing goals after scoring themselves to giving away two-goal leads. They own the dubious distinction of being the only team in the NHL unable to win a game in which they scored two or fewer goals (0-25-9).

“For me, what all can you really do?” Oates said when asked whether he thinks he will return next season. “All I’ve focused on is doing my job, doing the best I can, and I don’t worry about it.”

Alex Ovechkin, who won his third Hart Trophy last season and was the only player to reach the 50-goal plateau this year, said he would like to see Oates return as coach.

The relationship between the star player and coach appeared to shift in recent weeks as Oates said Ovechkin “quit” on a play that led to a goal by the Dallas Stars on April 1. Three days later, Ovechkin expressed frustration at having been utilized on a line with grinder Jay Beagle as his center for a month, saying, “Of course I can be angry about it, but I still have to play.”

But even with those recent comments, Ovechkin said Sunday he still trusts Oates and dismissed the notion he would have a prominent role in determining the coach’s future.

“We’ll see what happens, but for me and for the team, I don’t know how many times we talk about the changes. . . . It’s not about me or [Nicklas Backstrom] or somebody else. It starts on top, and if they want to change, they have to change,” Ovechkin said. “If they want to talk to me about it, I will talk, but I’m not going to say something like we have to change coach, we have to make trades or we have to do something with George.

“If it’s going to happen, I’m going to talk to the team or somebody out there. I’m not going to say it in the media,” Ovechkin continued. “I respect everybody in this organization. They do lots of things, and I’m not going to say bad things not to their face.”

Top defenseman John Carlson issued confidence in Oates as well, stating that the players “should take responsibility” for the Capitals falling short of the playoffs this season. His partner on the team’s No. 1 pairing most of the season, Karl Alzner, praised Oates’s understanding of the game.

“I would go as far as saying that Oatesy is a hockey genius when it comes to the technical side of the game,” Alzner said. “I don’t think anyone thinks the game as good as he does or as technical as he does.”

Troy Brouwer also complimented Oates as someone who “studies the game” and has given the players all the information they can to win games but stressed that choices about what direction the Capitals take are not up to him.

Goaltender Braden Holtby, who finished with 32 saves in the season finale, offered a similar sentiment about simply being part of the equation, not a deciding party in Oates’s future.

“I’m in no position to question a head coach that’s not — I’m paid to stop the puck. That’s what I do. That’s what I want to do. That’s strictly the only thing I want to do,” Holtby said. “That’s what management and ownership is for — to make those decisions to make the team better.”

Capitals notes: Marcus Johansson missed Sunday’s game with an injured left hand or arm. . . .

Mike Green sat out a fourth straight game with what is believed to be an injured right hand. . . .

Jack Hillen and Patrick Wey missed their ninth and seventh games, respectively, with what are believed to be concussions.