CHICAGO — The hats flew onto the ice. The crowd roared. Patrick Kane had just notched both a hat trick and his 100th point of the season with the same flick of the blade, putting Chicago up by six goals. The Blackhawks celebrated. The Bruins looked glum, beaten, humiliated. They knew that this game was shaping up to be a huge loss for a team coming off a huge win.

And it would indeed end up a loss, with poor decisions leading to defensive miscues leading to goals against over the first 35 minutes. But the Bruins didn’t fold, scoring four unanswered goals in just 10:07 of ice time, starting with David Pastrnak’s breakaway with 15.6 seconds left in the second.

It wasn’t enough. Their comeback fell short, and the Bruins lost, 6-4, at the United Center on Sunday afternoon.

But — and this was a point stressed over and over in the postgame dressing room — the Bruins do remain alive for the postseason. They can still get into the playoffs without help from anyone else, though that would take three wins at home this week against Carolina, Detroit, and Ottawa.

“We just have to realize how desperate we have to play the rest of the season,’’ Brad Marchand said. “We need three wins. It comes down to that. So we have to understand the situation we’ve put ourselves in and play desperate the rest of the way.

“There’s only three games left. They’re all must-win. We can’t dwell on this game. The first half was obviously a bad effort, some poor decisions. But we have to park it, regardless of how bad we played.’’

For now, the Bruins remain on the outside of the playoff structure, the same place they found themselves Sunday morning after Detroit beat the Maple Leafs on Saturday.

It wasn’t all bad, though. The Bruins have shown, over the last two games, that they have found their offensive stroke, at the same time that they have shown their defensive deficiencies. After scoring six goals against the Blues, the Bruins came back with four against Blackhawks goalie Scott Darling, putting 46 shots on goal. Those 10 goals matched the output from their previous seven games.

It started with that goal by Pastrnak, his 13th of the season. The second came with 4.5 seconds remaining, by Patrice Bergeron, who added his second 2:39 into the third. Marchand was next, as the Bruins put 21 shots on goal in the second and 17 more in the third, a period that Bergeron called, “a perfect example of how we need to play.’’

“We thought anything can happen at that point,’’ Marchand said. “We were feeling pretty good about ourselves and still [had] half a period left.’’

They had opportunities. They couldn’t cash in any more than they already had, even after pulling the goalie with 2:42 to play.

Still, it felt like a different game than it had two minutes into the second when Tuukka Rask skated off the ice, yielding the net to Jonas Gustavsson.

“For me, I thought we had our legs,’’ coach Claude Julien said. “I thought we competed hard. We didn’t have our brains tonight. We made some real poor decisions. That, to me, is what cost us. It’s more about the decision-making has got to be better.

“When you look at the kind of mistakes we made, outnumbered situations, pinching at the wrong time, making those low-percentage passes or plays that turn into a counter that ends up in our net. So those are things that are probably the major thing that really hurt us tonight.’’

The first goal, from Artem Anisimov, came off a whiffed shot by Artemi Panarin. But instead of the chance fizzling, the puck went to Anisimov, who beat Rask at 13:14. It was a bit of a fluky goal, some good luck for Chicago. The rest? Those were not flukes.

“It’s really disappointing,’’ Bergeron said. “It cost us the game. It’s pretty obvious that if we would have played the way we played halfway through . . . we can’t wait for them to score four or five goals to get going. Especially at this time.’’

Kane got the first of his three at 18:31 off a turnover from Joe Morrow at the offensive blue line. It was Kane again 54 seconds into the second, and after that, Jonathan Toews on a two-on-one with Marian Hossa at 2:00. That was the goal that ended the night for Rask.

But it didn’t stop. Panarin got his at 5:17. Kane got his third at 14:16.

“We just gave pucks away a lot, gave them some room to make plays,’’ Rask said. “Obviously, they’re a good offensive team, and they will make those plays. It resulted as a 4-0 deficit. We battled back, though, but gave up 6-0. Kind of tough to come back.’’

That was when the embarrassment was at its height, down six goals to none in a game the visitors needed. It didn’t end there, for the Bruins’ offensive chances or for their playoff hopes. Still, the hopes are waning. The shot at the postseason looks increasingly slim, just as it did in the final games of last season, when the Bruins missed the playoffs for the first time since 2007.

“Win our last three games, we’re in the playoffs,’’ Torey Krug said. “We know that. We know what’s at stake. We’ve got to take them one game at a time. I think last year we got caught up looking a little too far ahead of ourselves, but it’s a different story this year. We’re going to take it one game at a time, learn from everything that’s happened so far.’’