Yankees general manager Brian Cashman can’t turn off his sell phone just yet. Try as they might, the Yankees have not yet proven this roster has staying power to make a run at a postseason berth.

A winning homestand is still possible, but a great one is not after Saturday’s 2-1 loss in 12 innings to the Giants. The Yankees are 5-4 with one game remaining in the homestand that was somewhat billed as the defining one in the buy-sell saga as the Aug. 1 non-waiver trade deadline approaches. Cashman did not respond to an email seeking comment before the game.

“I think [Sunday’s] a really big game for us,’’ Joe Girardi said in what seemed like the nth time since returning from the All-Star break. “We’ve got to make up ground. And we’ve been around .500 and we’re staying there, so.’’

This next series of “must-win” games will be played with a tattered bullpen. Andrew Miller, Aroldis Chapman and Dellin Betances — in that unusual order — all pitched but the Yankees couldn’t break a 1-1 tie in a game that started with an apparent mismatch of Ivan Nova against Johnny Cueto, who was moved up a day in an effort to help the Giants end a six-game losing streak.

With the vaunted Yankees bullpen spent, Anthony Swarzak came on in the 12th and gave up a leadoff double to Trevor Brown. Mac Williamson singled him in with the go-ahead run.

“It was a situation that I knew I wasn’t going to be able to make too many mistakes,’’ Swarzak said. “Unfortunately, I gave up two hits, both on pitches elevated in the zone.’’

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Williamson’s leadoff home run in the fifth had tied the game after the Yankees scored an unearned run off Cueto in the fourth aided by Williamson’s error in right.

The Yankees, who were 0-for-10 with runners in scoring position, left 11 runners on base. Still, they had their chances.

With one out and the bases loaded in the 10th, Brian McCann flied out to shallow left and Starlin Castro fouled out to right.

“I got to do a better job,’’ McCann said. “Trying to get it into the outfield, got a pitch I liked, I just didn’t hit it hard enough. This one hurts. When I come up with bases loaded, less than two outs, I gotta get that job done, It’s just disappointing I didn’t come through.’’

In the eighth inning, McCann was off and running from first on a liner to left by Castro that was caught by Angel Pagan, who doubled off McCann at first base. McCann thought it was going to drop in front of Pagan. “I did, I was trying to get to third base. I thought it was going to get down.’’

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The Giants nearly scored the go-ahead run in the 11th off Betances on a most unusual occurrence. With two outs and Pagan on third, Betances, who was supposed to be given the day off, was told to intentionally walk Brandon Crawford, but his pitch sailed over McCann’s head in what would have been a wild pitch on an intentional walk but Pagan didn’t dash home.

“That was nerve-wracking right there,’’ Betances said. “I tried to lob it. It was nowhere near McCann. Thank God it kicked right back to him.’’

So the pressure apparently remains on the Yankees to make up ground in the standings or face a breakup by the trade deadline.

Carlos Beltran said winning the next game will be “as important as it was today.’’ As for the ramifications of losing, he added: “We don’t worry. That’s not in our hands. We have to go out and perform but the organization is going to make whatever decision it’s going to make. So we cannot worry about that.’’