BOSTON -- José Abreu wore the disappointment of the final score on his face.

The White Sox had just sustained a 6-5 walk-off loss to the Red Sox, and Abreu was thinking about the first hit of the inning that began the comeback rally.

• Box score

Andrew Benintendi belted a ground ball past Abreu at first base and into right field at 101 mph, according to Statcast. He stretched the hit into a double, an outcome that only had a .680 xBA, and went on to score the winning run. Abreu thought he should have played closer to the line.

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

The White Sox led the Red Sox by one entering the eighth inning. With Kelvin Herrera on the mound, pinch-runner Marco Hernandez, who would play the role of spoiler in the ninth, scored the game-tying run off an Eduardo Núñez single.

Reliever Jace Fry led off the bottom of the ninth with the double to Benintendi. He caught J.D. Martinez swinging for the first out and got Rafael Devers to ground out to first. Benintendi advanced to third on that play. After Fry intentionally walked Xander Bogaerts, who stole second, he also intentionally walked Jackie Bradley Jr. (once he was ahead in the count, 3-1) to load the bases with two down.

Hernandez then smacked a ground ball to shortstop Tim Anderson and beat out the throw to Abreu to drive in the Red Sox’s game-winning run.

“I thought Timmy did everything he could to try to make that play,” manager Rick Renteria said. “The young man can run pretty well. He ended up doing a nice job of getting the bat on the ball there. I thought honestly we gave ourselves the best chance there with the matchup and see if Fry could go in and finish it off, keep us there.”

While Abreu held himself accountable for the final outcome, starting pitcher Lucas Giolito pointed to his performance earlier in the game. Giolito pitched 5 2/3 innings, allowing three runs off six hits (including a home run to Bradley Jr.), handing out four walks and striking out seven. But he ran into a jam in the sixth inning, in which he walked Michael Chavis with the bases loaded to tie the game, 3-3.

That would end Giolito’s night. Evan Marshall struck out Nunez in the next at-bat to end the inning.

“I let them come back and tie it up like two or three times,” Giolito said. “For me, just an unacceptable performance. I need to be able to bear down there at the end of my outing and get through it.”

He added, “From my perspective, the offense is working their butt off and they give me the lead a couple of times. I’ve got to hold on to it. I’ve got to go out there and finish strong, and I didn’t do that.”

The White Sox had produced enough firepower to be in position to win the game, but two monster home runs were not enough to maintain the lead. Yoán Moncada jump-started the offense in the second inning with a two-run blast off Eduardo Rodriguez that sailed 390 feet to left field, according to Statcast. Moncada's 13th home run of the season was his first since going back to back on June 4 and 5 against the Nationals.

Four innings later, Abreu tied Jermaine Dye for seventh all-time in White Sox history with his 164th career homer -- a 430-foot shot off Rodriguez with an exit velocity of 110.7 mph. Total travel time out of the park: a mere 4.6 seconds. If one of the sponsored signs posted atop the Green Monster in left field hadn't been there to repel the ball, there is no telling how far Abreu’s home run would have soared into the streets of Boston.

“To hear my name next to Jermaine Dye is some very good company,” Abreu said. “It’s always an honor to be on the list of all-time leaders.”

The White Sox lost their third walk-off game of the season. They moved to 10-10 at Fenway Park since the start of 2014.