CLEVELAND — Maybe David Price meant next October.

Or the one after that. Or October 2019.

Some future October other than this one.

Shortly after signing a seven-year, $217-million contract last offseason, the Red Sox lefthander put his past postseason failures squarely on the table by saying “I think I was just saving all my postseason wins for the Red Sox.” Then he came up small again in the sport’s biggest month.

Price failed to get out of the fourth inning and Cleveland righthander Corey Kluber pitched seven shutout innings Friday as the Indians beat the Red Sox, 6-0, in Game 2 of their American League Division Series. That sent Boston home in a 0-2 hole.

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“Backs against the wall,’’ Red Sox manager John Farrell said. “It’s pretty clear what lies ahead of us.”

The series moves to Fenway Park on Sunday afternoon, with Boston’s Clay Buchholz taking on Cleveland’s Josh Tomlin — and the Red Sox facing elimination after Price’s poor outing.

“That stung for sure, but I’ll be ready whenever my number’s called again,” said Price, 0-8 with a 5.74 ERA in nine career postseason starts. “I know my number’s going to get called again to pitch again in 2016, and I’ll be ready. I want it for sure and I know these guys will give it to me.”

The Red Sox, who led the majors with 878 runs, have been outscored 11-4 in the series by the Indians, who were second in the American League with 777 runs.

“Our confidence isn’t altered,” said Price, who allowed five runs and six hits in 3 1⁄3 innings, the shortest postseason start of his career. “This is a very confident group, even though we’re down 0-2 right now. We’re all right.”

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Kluber, like Price a former AL Cy Young Award winner, was that and more. Pitching on 10 days’ rest because of a quadriceps injury suffered toward the end of the season, Kluber — who made $4.5 million compared to Price’s $30 million this season — allowed three hits and three walks and struck out seven.

Kluber departed with a 6-0 lead, two on and none out in the eighth, giving way to Dan Otero, who retired the side.

“You go through that lineup and you don’t give up runs,” Cleveland manager Terry Francona said of Kluber, “you’re pitching.”

The sellout crowd of 37,842 at Progressive Field was whipped into a noisy, red towel-waving frenzy before the game as LeBron James, surrounded by teammates Richard Jefferson, James Jones, Dahntay Jones and J.R. Smith from the defending NBA champion Cavaliers, gave a surprise pep talk. He ended it by pointing to the Indians’ dugout and saying, “We’re here for those guys there.”

Lonnie Chisenhall had the towels twirling again in the second inning with a three-run homer off Price, the highlight of a four-run inning that gave Kluber (18-9 with a 3.14 ERA this season) more than enough offensive support.

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His ability to pitch deep into the game was especially important, given the way Francona used his bullpen in Thursday’s 5-4 victory. In that game, Francona brought in stud lefthander Andrew Miller in the fifth and had him throw two innings before using closer Cody Allen for a 1 1⁄3-inning save. Francona preferred not to use either Friday if he could avoid it.

Kluber made that possible.

And Price?

“I know good things are coming to me in October baseball, I know that,” he said. “I didn’t have good things happen today and the Indians are playing well. Kluber threw the ball extremely well today. They had good things happen. That’s part of it.”