BOSTON -- With the hours ticking down to Wednesday’s 4 p.m. ET Trade Deadline, an all-too-familiar theme developed for the Red Sox on Tuesday night at Fenway Park.

A starting pitcher -- David Price this time -- didn’t go deep enough into the game. And the relievers, asked to handle a heavy load, couldn’t get it done.

In a game the Red Sox led twice, they wound up taking a 6-5 loss to the Rays in the opener of a three-game series.

• Box score

Red Sox manager Alex Cora has said continually that the biggest key for his team to have a complete resurgence is for the starters to go deep into games. Last week, there was an encouraging glimmer of hope, when the rotation went a season-high six straight games of pitching six innings or more.

But in the past two games -- both losses -- Chris Sale got hit around in 5 1/3 innings, and Price was removed after 4 1/3 on Tuesday.

“It’s always tough,” Cora said. “It’s not like they aren’t trying, it’s just a bad night as far as location [for Price]. But, the other guys [in the bullpen] have to step up. So, we’ve got to do a better job there.”

The offense, which has been relentless for the Red Sox all month, had the tying run in scoring position in the final three innings. Most enticing was when Rafael Devers stepped up with the bases loaded and two outs in the eighth. But the emerging star lined out to left on a 97.9-mph fastball by Emilio Pagan.

With two on and two outs in the ninth, Christian Vázquez had a chance to win the game and got a hanging slider middle-middle on 2-2 from Pagan. He got under it and flied out to deep left to end the game.

Then again, it’s not fair to expect the offense to continually bail out the pitching staff, which has happened many times during a 15-9 July.

“We were patient enough to get our matchups. We got the tough lefties out of the way, so we had the lefties against the righties,” Cora said. “They made a good play up the middle on the ground ball by Mookie [Betts], and then Raffy missed a few pitches and had that fly ball. That last pitch to Christian, he missed it.”

It was that kind of night, as the Sox left 11 men on base and went 3-for-15 with runners in scoring position.

Making the loss all the more frustrating is that Tampa Bay is one of the teams Boston is jockeying for position with in the American League Wild Card standings. The loss put the Sox 1 1/2 games behind the Rays and two back of the Athletics.

The night started with good vibes as Price took a 3-1 lead into the fifth in his rematch from last week against Rays ace Charlie Morton. But things changed quickly. Travis d’Arnaud and Avisail Garcia unloaded for solo shots to tie the score. When Price then gave up back-to-back hits to Michael Brosseau and Nate Lowe to put runners on second and third with one out, he was removed in favor of Marcus Walden, and Tampa Bay quickly took the lead on a fielder’s choice grounder.

Price was the best starter the Red Sox had prior to the All-Star break, going 7-2 with a 3.24 ERA. But in his past five starts, Price is 1-2 with a 5.55 ERA and has gone five innings or fewer in four of those outings.

“When the guys go out there against a really good pitcher, a guy that’s leading our league in ERA and they give me that lead, to give that lead right back right after, that’s tough,” Price said. “It’s been a grind over my past five or six starts. Outs are tough to get. It’s been tough just throwing strikes. Physically, today was the best I’ve felt in a while. I feel like I have some stuff to address these next four days before I pitch in New York [on Sunday], but I think it’s going to get better.”

Even after Price’s exit, and blowing the lead the first time, the Sox still put themselves in position to win the game. In the bottom of the fifth, Rays manager Kevin Cash made an interesting strategical decision, taking out Morton with two outs and one on, meaning the American League Cy Young Award candidate couldn’t qualify for the win. Lefty Adam Kolarek came on, and Andrew Benintendi drilled his first pitch over the Monster for a two-run shot that put the Sox back up at 5-4.

This should have been a game-turning moment for the Red Sox. But the bullpen gave it right back even after Walden opened the sixth by retiring the first two batters. After Walden gave up a walk and Josh Taylor surrendered a hit, Cora went to Colten Brewer, and Garcia mauled a two-run double high off the Monster to make it 6-5, Tampa Bay.

“That can’t happen,” Cora said. “For us to take it to the next level, we’ve got to put guys away. and that was a big shutdown inning for us. We’ve got to go back tomorrow and try to do it again.”

By then, perhaps the pitching staff will have the reinforcements needed to make a deep run.

As the Red Sox left Fenway Park late Tuesday night, president of baseball operations Dave Dombrowski was officially on the clock.

“We aren't where we want to be in the standings, but all in all, for the way we started, the way we played at home, we haven’t put our best foot forward yet,” Price said. “That’s a good sign considering where we are in the standings right now. I’ll look forward to seeing what happens tomorrow. I think everyone else is, too.”