BOSTON — In what has become a predictable scene, the Mets played the rubber game of a series Sunday and barely showed up.

Carlos Carrasco was extremely hittable and didn’t even survive through the third inning, but the veteran right-hander was only part of the Mets’ problem.

There was also the matter of a lineup that had chances, particularly late in the game, and failed to produce against the Red Sox in a 6-1 loss at Fenway Park.

Six games remain for the Mets before the Aug. 1 trade deadline and even winning them all would leave this crew below .500, only underscoring the need for team officials to move toward sell mode — if they aren’t already there.

The Mets (46-53) have lost five of nine games since the All-Star break.

In rubber games of series this season they are 4-9, a number if flipped would have them sitting in positive territory in the win/loss column.

Daniel Vogelbach’s pinch-hit strikeout on 12 pitches in the eighth was the last gasp for the Mets, who had put two runners on base in the inning.

The Red Sox had four runners thrown out on the bases, allowing the Mets at least a puncher’s chance in the late innings.

“We had a couple of chances to get back in it, we just couldn’t get that hit,” manager Buck Showalter said. Carrasco, in a second straight awful outing, allowed five earned runs on 10 hits and two walks over 2 ¹/₃ innings.

It was the fifth time in 14 starts this season Carrasco allowed at least five earned runs.

“The problem was I was getting behind in the count,” Carrasco said. “I have just got to go throw strikes.”

Adam Duvall delivered an RBI single in the first that produced the game’s first run.

The inning might have been worse for the Mets if not for Jarren Duran’s decision to break for the plate on Pete Alonso’s throw that sailed off Carrasco’s glove at third base with the pitcher covering.

Mark Canha retrieved the ball and threw a strike to the plate to nail Duran, who had advanced first-to-third on a ground out.

Carrasco was visited by the trainer following the play (which involved a collision with Duran), but remained in the game.

Carrasco twisted his ankle on the play, according to Showalter.

“It looked like it was going to be a potentially challenging night [for Carrasco] beforehand, but I’m sure that didn’t help any,” Showalter said.

The Red Sox managed seven straight hits against Carrasco and Drew Smith in the third to score four runs and extend their lead to 5-0.

Justin Turner doubled leading off and went to third on Rafael Devers’ single.

Duvall followed with an RBI double, on which Devers was thrown out rounding third base.

Triston Casas followed with an RBI single that put the Mets in a 3-0 hole and after Connor Wong and Enrique Hernandez singled to load the bases Carrasco was removed.

Yu Chang’s single off Smith gave the Red Sox a fourth run and Smith’s wild pitch extended that lead to 5-0.

Canha also threw out Casas attempting to stretch a single into a double in the fifth.

Canha, according to Sports Info Solutions, didn’t have a direct assist as a left fielder in his previous 3,178 innings playing the position.

Canha finished the game with three.

“They kind of just fell in my lap,” Canha said. “Just playing the game and trying to make all the right plays and … try to play an aggressive outfield and it just kind of happened.”

Francisco Lindor’s RBI single pulled the Mets within 5-1 in the sixth.

But the Mets wasted an opportunity to jump back into the game (with runners on first and third) when Jeff McNeil was retired and Alonso and Mark Vientos struck out in succession.

Danny Mendick’s walk began the rally.

Devers launched a solo homer off Dominic Leone in the seventh that buried the Mets in a 6-1 hole.

The run against Leone was the only one charged to Mets relievers over 5 ²/₃ innings.

But that group has received plenty of usage over the past two days, which included the resumption of a suspended game from Friday.

“Some good things were done out of the bullpen, but you hate to pitch that many innings there,” Showalter said. “Fortunately we have a day off, but you can come out of that limping too. It’s a challenge when you get a shorter start.”