NEW YORK -- With each pitch, it became increasingly clear that Jeurys Familia was losing steam. Familia had been excellent in the sixth inning on Sunday, allowing the Mets to maintain a one-run lead over the Padres. But the seventh was different. Just that quickly, Familia lost the strike zone, with ball after ball flying not particularly close to it.

As Familia labored, manager Luis Rojas remained immobile by the dugout steps. Murmurs rippled through the crowd as Jurickson Profar battled back from a 1-2 count to draw the second walk of the inning. Still Rojas did not move. Only after Familia followed with a bases-loaded, game-tying, four-pitch walk to Tommy Pham did the manager finally relent, calling on Jacob Barnes -- not one of the Mets’ high-leverage relievers -- to face Fernando Tatis Jr.

Tatis promptly hit a grand slam to sink the Mets in a 7-3 loss at Citi Field.

“It was a tough game today,” Rojas said. “We feel that we can do this, we can bridge with that plan, using Familia for two [innings]. … It was a tough one.”

Rojas was trying to strategize despite his heavy recent reliance on Seth Lugo (three straight games), Edwin Díaz (two in a row) and Aaron Loup (two), all of whom were potentially unavailable. The Mets were also perhaps without Miguel Castro, who hasn’t pitched since leaving Friday’s game with a minor neck injury.

Despite all that, Rojas had at least three ways to avoid the matchup -- Barnes vs. Tatis, an early National League MVP Award favorite -- that beat the Mets.

1) Let Lucchesi pitch deeper
One of the Mets’ more promising recent trends has been the improvement of Joey Lucchesi, who recovered from a leadoff homer by Pham on Sunday to thrive in the middle innings. More than that, Lucchesi appeared to grow stronger as the game wore on, striking out five of his final six batters.

But as soon as Lucchesi finished off the last of those strikeouts, both Barnes and Familia began tossing in the bullpen. Lucchesi’s spot was due up fourth in the bottom of the fifth, and Rojas did not want to sacrifice an at-bat against Padres starter Chris Paddack, who had been nearly unhittable before serving up José Peraza’s two-run homer moments earlier.

“We just wanted to score so we could separate the game,” Rojas said. “We felt that we weren’t going to win 2-1, knowing the kind of offense this team can have. So we were just looking to score as their pitcher was going the third time through the lineup.”

Even so, with another starting pitcher on the mound, the situation might have been different. The Mets have been firm about not letting Lucchesi face any batting order the third time through, no matter how well he’s pitching. On Sunday, that meant cutting Lucchesi short despite five of his most dominant innings of the year, which lowered his ERA to 1.56 over his last four starts. More than the pinch-hit opportunity, Rojas said he did not want Lucchesi to face Tatis and Manny Machado three times in a game.

If the Mets wouldn’t let Lucchesi see a lineup three times on Sunday with a short bullpen, then when might they relent? Lucchesi was left wondering that, as well.

“I want to pitch as long as I can,” the lefty said. “I only threw 72 pitches. I’m not tired. I wasn’t tired at the time. I told them I wanted to keep going, but you’ve got to respect the manager’s decision. That’s all I can do. I told them I want to keep pitching, but I guess I’ve got to keep showing them I can get through the order three times, and I can pitch, man.”

2) Go to Barnes sooner
As Familia labored in the seventh, Barnes believed he was warming to face Pham with two outs. But when Familia walked Profar to load the bases, Rojas did not budge. His thinking was that Familia had executed credible “chase pitches” that Profar simply did not chase. Rojas believed Familia -- who had already thrown 37 pitches at that point -- still had strong command of his repertoire, and the right-hander was a better matchup against Pham.

That proved incorrect when Familia missed the strike zone by about a foot on each of his first two pitches to Pham. Only one of the four balls he threw even came close to the zone.

“They were trying to let him get out of his situation, and unfortunately, Pham got a walk there,” Barnes said, speaking on behalf of Familia, whom the Mets did not make available for comment.

3) Use someone else
Despite his 5.40 ERA, Barnes survived a recent roster cut when the Mets optioned Sean Reid-Foley to Triple-A Syracuse. Since spring, the Mets have shown some favoritism toward Barnes, who -- unlike Reid-Foley -- is out of Minor League options.

But the Mets still did not have to use him in one of the highest-leverage spots imaginable. Drew Smith, who struck out Tatis later in the game, also was available to pitch. So was Trevor May, who has not appeared in a game since June 6. Rojas wanted to save May for a potential save situation in the ninth, despite not having any guarantees that such a chance would exist.

“We needed May to close the door,” Rojas said in explanation.

As such, Rojas opted to go with Barnes, who allowed homers to Tatis and Machado to increase his ERA to 6.27 and send the Mets to a dispiriting loss.