BOSTON — The Red Sox have a David Price problem.

He can’t pitch in the playoffs and he can’t pitch against the Yankees.

That’s a rough combination for the southpaw, whose struggles in both departments were clearly on display in the Yankees’ 6-2 win in Game 2 of the ALDS that evened the series Saturday at Fenway Park.

Price failed to even get out of the second inning in his first playoff start in two years. He gave up three runs in just 1 ²/₃ innings before he was yanked, replaced by Joe Kelly and booed off the mound.

Not ideal for someone who may be asked to start again this series — and has four years and roughly $127 million left on his contract.

“I didn’t execute enough pitches and that was that,’’ Price said. “They make it tough for me. Knowing that, you have to go out there and execute pitches in big spots in counts. And that’s something I wasn’t able to do. … But my spirits aren’t down, my confidence isn’t down. I’m looking forward to getting back out there and getting another opportunity.”

Following the latest debacle, Boston manager Alex Cora said Price would remain in the rotation, but he could be used out of the pen, since he just threw 42 pitches.

“He’s part of what we’re trying to accomplish and we count on him,’’ Cora said.

Price’s latest fiasco started when Aaron Judge belted a 445-foot homer over the Green Monster in left-center to give the Yankees a 1-0 lead in the first.

Gary Sanchez then opened the second with another homer. Price got a pair of groundouts from Didi Gregorius and Miguel Andujar, but he walked Gleyber Torres to extend the inning.

Brett Gardner worked another walk after being behind 1-2. Price begged for a 2-2 pitch that was inside and Gardner walked on the next pitch.

That forced Cora to get Kelly up in the bullpen, as Price faced McCutchen.

McCutchen hammered a ball off the Monster that likely would have been a three-run homer anywhere else, but went for an RBI single.

The hit ended Price’s outing, with the Yankees leading 3-0.

Since the start of 2016, the lefty is 2-7 with a 7.71 ERA against the Yankees.

He also had a 10-game stretch in the postseason in which he had a 5.90 ERA. That ended a year ago with two solid outings out of the bullpen with the Red Sox, but his October issues clearly have not gone away.

“I just want to win,’’ Price said. “That’s it. My main goal is to win in the playoffs, to win a World Series. Whatever I have to do to help us do that, I’m fine with. … I know I’m more than capable of winning games as a starter in October. That’s what I look forward to doing.’’