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BOSTON — At this point, the Yankees may just have to tip their cap and call the Red Sox their Daddy.

The best thing they had going for them by the time they headed back to New York was that they did not have to see the Red Sox again until August.

A dud of a weekend mercifully came to a close late Sunday afternoon, but not before the Yankees offered one last whimper on Father’s Day in a 2-0 loss as they got swept out of Fenway Park.

Facing the Red Sox (37-36) on back-to-back weekends, the Yankees (42-28) dropped five of six and seemingly gave life to their rival’s season.

“It sucks losing to the Red Sox. We never like that,” manager Aaron Boone said. “But it’s why teams don’t win 120 games. We’re really good. I think that’s going to continue to show itself. We had a tough weekend. And frankly, had a chance to potentially win all the games, even back at home against them. Credit to them, they were a little bit better than us this weekend.”

In The Bronx last weekend, it was pitching that failed the Yankees. At Fenway, it was their lifeless bats, plus a costly baserunning miscue in each of the past two games here.

The Yankees arrived in Boston on Friday coming off a sweep of the Royals that lifted them a season-high 17 games above .500. They left having scored four runs in three games as they suffered their first sweep of the season in their 23rd series.

“Just couldn’t really get anything going,” said Aaron Judge, who finally looked human for a weekend while going 1-for-12 with a home run and nine strikeouts. “At home, we swung the bats well. Here, we just couldn’t string those couple at-bats together and drive some runs across. They scored first every game to put us in a hole and just weren’t able to dig out of it. Next time we got to put a little more pressure on them and get that lead to start.”

Brayan Bello became the latest Red Sox starter to stifle the Yankees, firing seven shutout innings with eight strikeouts while scattering just three hits.

In 21 ¹/₃ innings against Red Sox starters this weekend — Garrett Crochet, Hunter Dobbins and Bello — the Yankees mustered just one run, which was Judge’s ninth-inning home run on Friday night.

That proved to be Judge’s only hit of the weekend as the red-hot slugger cooled off for a series. He went 0-for-4 Sunday and the only time he did not strike out, he hit into a double play that killed a rally in the eighth inning.

But the Yankees could not pick up their best player.

Their best chance of scoring off Bello came in the third inning, when they had runners on first and second with two outs and Jazz Chisholm Jr. at the plate. But Ben Rice took too big of a lead off second base as he tried to steal third, except Bello never started his windup and instead threw to second to nail Rice and escape the jam.

It was all too similar to Jasson Domínguez getting caught flat-footed between second and third to kill a rally on Saturday night, when the rookie outfielder forgot how many strikes there were.

“Especially when you’re playing the Red Sox, you always want to put your best foot forward,” Boone said. “They took us down this weekend, back-to-back weekends. So you hate that, but we have a really good club. Just didn’t play our best here this weekend.”

Their weekend at Fenway Park was so rough not even Max Fried — who had been the definition of a stopper prior to Sunday — could save the Yankees from a sweep. He tossed seven innings of two-run ball, but even that deficit proved insurmountable for the Yankees, who did not take a lead all weekend.

“Long season,” Boone said. “We’re in the middle of a tough stretch right now, obviously [playing] 16 [days] in a row. We get home [Monday] and start anew and hopefully get the bats going and have a big home stand.”