Tyler Austin of the Yankees connects on a third-inning single...

Tyler Austin of the Yankees connects on a third-inning single against the Boston Red Sox at Yankee Stadium on Thursday, Sep. 29, 2016. Credit: Jim McIsaac

Going into their game against the Red Sox on Thursday night, the Yankees nee ded a few things to happen if they were going to make the American League wild-card game.

They needed to win four in a row. They needed the Orioles to lose four in a row. They needed the Tigers to lose three of four. They needed the Mariners to lose two of four.

Oh, and then the Yankees needed to win a tiebreaker game or games.

All that just to get back to where they were a year ago — playing in the wild-card game.

The Yankees were eliminated from their quixotic quest at about 9:45 p.m. when the Orioles completed a 4-0 win over the Blue Jays in Toronto. It didn’t matter that the Yankees later beat the Red Sox, 5-1, to sweep the three-game series against the AL East champs.

“It’s not what we wanted,” Joe Girardi said. “It’s pretty quiet in there. Probably the quietest I’ve ever seen it after a win.”

It was the Yankees’ fourth straight victory. Still, there will be no playoffs in the Bronx this year unless you count the Yankees’ soccer co-tenants, NYC FC. That club clinched an MLS postseason berth on Saturday.

No conflicts here: NYC FC can have Yankee Stadium for whatever date it wants when its postseason opens in late October.

By then, the Yankees should have completed their dissection of what happened in 2016. It’s not supposed to be in the Yankees’ DNA to accept failure. Girardi said he doesn’t consider a playoff-less season a success.

But the Yankees and their fans knew the playoffs were an extreme long shot when the team completed its much-needed sell-off before the Aug. 1 trade deadline.

The Yankees were 52-52 then. They are 83-76 now, which means they’ve played .563 ball since surrendering the season by dealing away Andrew Miller, Carlos Beltran and Ivan Nova to go along with the earlier trade of Aroldis Chapman.

Would the Yankees be a playoff team now if they hadn’t made those deals? Doesn’t matter. They did what they had to do to get off the treadmill of being just good enough to sniff the postseason but not good enough to be a championship contender.

The heavy lifting for general manager Brian Cashman will begin again after Sunday’s season finale.

For all the talk of the Baby Bombers, Gary Sanchez looks like the only sure thing, and he needs to work on reducing his passed balls. Aaron Judge was a strikeout machine who didn’t prove he could handle major-league pitching before getting injured. Tyler Austin showed a knack for clutch home runs but will have to contend with Greg Bird for at-bats in spring training.

Luis Cessa, Bryan Mitchell, Luis Severino, Chad Green and some of the young relievers had moments. There is more to come on the farm, but maybe not for next year.

Girardi is on board with the youth movement. According to the manager, the Yankees’ future is so bright, he has to wear shades.

“I think there’s a lot of talent and I think there’s a lot more coming, which I think excites us all,” Girardi said. “You want to see all these kids develop and come up and have successful major-league careers.”

Perhaps Girardi should have taken his players, especially the younger ones, on a tour of the visiting clubhouse before the Red Sox arrived Thursday.

The carpet in the Red Sox’s temporary digs still had the stench of champagne from Boston’s division-title celebration on Wednesday night. It’s a sickening smell, and one the Yankees can’t wait to breathe in again in their clubhouse. It might take a while, though.

SUBSCRIBE

Unlimited Digital AccessOnly 25¢for 6 months

ACT NOWSALE ENDS SOON | CANCEL ANYTIME