BOSTON -- Sometimes, it really might be dangerous to schedule a promotion on the ice after a game.

The Boston Bruins ran into one of those times on Saturday.

On Fan Appreciation Day, the Bruins continued their "shirts off their backs" promotion, rewarding TD Garden faithful who had won a drawing at the final home game of the season.

But before giving away their shirts, the Bruins may well have tossed away their shot at 2016 NHL playoffs -- a stunning 6-1 defeat at the hands of the Ottawa Senators that led to the awkward shirt giveaway that included boos from those left in the stands.

"I don't think there's any words for it," Patrice Bergeron said after the Senators, who didn't make the playoffs, scored four goals in an 8:18 of the second period to leave the Bruins close to elimination. "I think we all know it's disappointing, and there's not much to be said right now."

The Senators poured the four goals on nine shots against backup goaltender Jonas Gustavsson, playing because Tuukka Rask was sick. They added a pair of empty netters late.

"It's unacceptable, the way that we showed up, and you can't win games if you do that," Bergeron said. "So we got it coming I guess, by not showing up. We did score the first goal, and we should've kept going at them, and we didn't. We let them get back in the game."

The loss eliminated the Bruins from third place in the Atlantic Division. The Detroit Red Wings lost to the Rangers in New York but took the tiebreaker because of regulation and overtime wins. The Bruins were left to wait to see if the Philadelphia Flyers were held to one point in two weekend games -- two points for Philadelphia and the Bruins were out for the second straight season. One point and the Bruins would have the tiebreaker and meet the Washington Capitals in the playoffs.

Failing to make it would seemingly leave coach Claude Julien's job status shaky, after a 42-31-9 season -- just 17-18-6 at home.

Rask was on the ice before the game but did little in warmups as emergency recall Jeremy Smith dressed. Gustavsson, in his first start since March 18, was sharp in a 17-shot first period but then the roof caved in.

"I found out pretty much almost as soon as I got here," Gustavsson said. "I got the word that he was sick and there was a big chance that I was playing and a few minutes later they said I was playing. So, it was just about getting ready as another game. I felt pretty good going into the game."

David Pastrnak gave the Bruins an early lead but James Neil, Zack Smith, Matt Puempel and Mika Zibanejad scored in the explosion.

The Bruins went on a power play with 9:26 left and Julien pulled Gustavsson, Jean-Gabriel Pageau scoring shorthanded into the empty net from his own end. Smith then scored his 25th of the season shorthanded into an empty net later in the period.

"It wasn't about Boston today," said Ottawa coach Dave Cameron. "We knew what was at stake for Boston and we knew if we had any advantage in the game today, all the pressure was on them.

"No pressure on us other than to go out and be evaluated and play the right way and make sure that we can finish our season, disappointing not being in the playoffs, but finish it as strong as we could."

Gustavsson made 30 saves, while Andrew Hammond, severely tested in the third period, stopped 39 -- 18 in the third -- for only his seventh win of an injury-plagued season. He stopped the last 38 shots.

The Senators won three of the four games in the season series with Boston and finished the season 38-35-9.

The second-period onslaught left the home crowd stunned and booing -- loudly.

Old tough-guy rival Neil got the first goal, sliding home a rebound after Gustavsson made a nifty stop on Ryan Dzingel 1:42 into the second period.

Just 3:12 later, defenseman Erik Karlsson clearly aimed a slap-pass from the right point at the stick of Smith, who deflected it past Gustavsson. Karlsson picked up his league-leading 66th assist, his 82nd point in 82 games.

"I think 82 points says it, but at the end of the day both Karl and I are frustrated that we're not in the playoffs," Cameron said.

The booing started when Puempel back-handed his second goal of the season home, shaking Pastrnak off like he was not there. A giveaway by Adam McQuaid led to Mike Hoffman centering to Zibanejad for an easy redirect, Zibanejad's 21st of the season.

Pastrnak scored a goal that was challenged by Cameron, who thought the play was offside. But for the second straight game, Pastrnak had an early challenged goal stand.

NOTES: G Jeremy Smith, who has yet to play an NHL game, arrived just in time for the game and dressed as Boston's backup. ... The two empty net shorthanded goals scored by the Senators in the third period were only the third and fourth shorthanded scores against the Bruins this season. ... LW Zack Smith's two goals came in his 400th NHL game, while Bruins D John-Michael Liles played in his 800th. ... LW Loui Eriksson was the only Bruin to play in all 82 games with the team, while RW Lee Stempniak totaled 82 games between the New Jersey Devils and Boston. ... D Erik Karlsson and C Jean-Gabriel Pageau played in all 82 for the Senators.