Jose Abreu homers but takes blame in White Sox’ loss to Red Sox

BOSTON — Jose Abreu tied Jermaine Dye for seventh place on the White Sox’ all-time list with his 164th home run, a rocket that looked like it still was rising when it hit the banner for a car-rental company above the Green Monster in the sixth inning Monday at Fenway Park.

‘‘To hear my name next to Jermaine Dye is some very good company,’’ Abreu said after the Sox lost to the Red Sox 6-5 on a walk-off infield single by Marco Hernandez against Jace Fry with the bases loaded and two outs in the ninth. ‘‘It’s always an honor to be on the list of all-time leaders.’’

But Abreu was despondent, faulting himself for being out of position on a leadoff double by Andrew Benintendi into the right-field corner that started the Red Sox’ winning rally. Abreu said he should have been playing no-doubles defense.

‘‘We battled,’’ Abreu said through a translator. ‘‘All the guys did their jobs. I wasn’t ready for the Benintendi hit. It was my fault. I truly take responsibility because that was the winning run, and I could have done a better job.

‘‘In that situation, I need to be a little bit closer [to the line], especially considering the hitter.’’

Two intentional walks loaded the bases for the left-handed-hitting Hernandez. He rapped a chopper to the right of shortstop Tim Anderson, who had to go in and to his right, then throw across his body. Hernandez beat the throw.

‘‘[Anderson] made a great effort on a difficult ball,’’ Abreu said. ‘‘But that wouldn’t have happened if I caught the line drive by Benintendi.’’

It was a postgame full of looking in the mirror. Right-hander Lucas Giolito, who was coming off his worst start of the season at Wrigley Field, was better, especially when he got five of his seven strikeouts in the first three innings. But he was lifted after walking Michael Chavis with the bases loaded and two outs in the sixth, tying the score 3-3.

‘‘For me, just an unacceptable performance,’’ Giolito said. ‘‘I need to be able to bear down there at the end of my outing and get through it.

‘‘Just not making competitive pitches when I need to, 3-2 counts. They got the bat to the ball a few times. I was pitching in traffic a lot, so, yeah, it was one of those games.’’

Giolito has been an All-Star-caliber pitcher for most of the season, and this outing — three runs, six hits, seven strikeouts and four walks in 5‰ innings — certainly wasn’t horrible.

‘‘The outing as a whole is fine, but just at the end there, the sixth inning,’’ Giolito said. ‘‘Just trying too hard instead of just trusting and throwing the ball over the plate. I’m never happy when I walk in a run.’’

The loss dropped the Sox, who are in the midst of a two-week stretch facing playoff-caliber teams, to 36-40 overall and to 1-3 on a trip that started against the Rangers.

‘‘You have to be a good self-evaluator, and you have to hold yourself accountable for mistakes that you make,’’ Giolito said. ‘‘It’s just part of our team. We’re going to stay on each other. We’re going to stay on ourselves, most importantly, and learn from our mistakes and come back the next day.’’

Yoan Moncada hit a two-run homer against left-hander Eduardo Rodriguez, and struggling Yonder Alonso and Yolmer Sanchez had back-to-back RBI singles in the seventh to put the Sox in front 5-3. But the Red Sox scored a run in each of the last five innings. Evan Marshall allowed a homer for the first time this season to Mookie Betts in the seventh, and Kelvin Herrera yielded a tying single to Eduardo Nunez in the eighth.

Anderson saw his nine-game hitting streak come to an end with his worst offensive game of the season, going 0-for-5 with four strikeouts.

Still, Abreu blamed himself.

‘‘It’s heartbreaking to lose today because I feel like it was my fault that we lost,’’ he said. ‘‘Tomorrow, be thankful for another opportunity.’’