CLEVELAND — If there is any justice, first baseman Jose Abreu will have a strong June and July and represent the White Sox at the All-Star Game in Washington.

Abreu, a model of offensive production and consistency during his five seasons in the majors, hasn’t been to the Midsummer Classic since his first season in 2014, when he finished fourth in American League MVP balloting and was voted AL Rookie of the Year.

A career .300 hitter with at least 25 home runs and 100 RBI in each season, Abreu hasn’t played on a winning team yet. The Sox were 73-89, 76-86, 78-84 and 67-95 in his first four seasons, and they are a major-league-worst 16-37 after a 9-1 loss Wednesday to the Indians.

A respected leader in the clubhouse who says he wants to stay with the Sox after his contract runs out at the end of next season, Abreu is having another excellent season. Not that the losses, day after day and year after year, aren’t getting to him.

‘‘It’s difficult,’’ Abreu said through a translator. ‘‘We are not here to lose games. I’m not here to lose games. I wasn’t born to lose games.’’

He said that before the Sox lost to Indians ace Corey Kluber to complete a 1-5 road trip. After the game, the players talked things over while reporters waited 25 minutes for the clubhouse to open. When reporters walked in after meeting with Sox manager Rick Renteria, a somewhat-animated Abreu stood at his locker, talking to about a half-dozen Spanish-speaking players.

‘‘It was about us,’’ third baseman Yolmer Sanchez, whose 446-foot homer in the ninth prevented the Sox from getting shut out, said of the meeting. ‘‘We don’t like to say what we talk about, but it was about us.

‘‘Try to stay together, that’s the most important thing. Stay together and come together. If we win, we win together; if we lose, we lose together.’’

As old as the losing gets, Abreu believes in the Sox’ rebuild, so he sucks it up and maintains his place as the hardest-working guy in the clubhouse.

‘‘We understand that we are in a process, and we have faith and conviction in the process,’’ he said before the game. ‘‘We have to be patient. Sooner rather than later, we want to start winning more games.

‘‘We have to patient because we’re on the process to be a successful team in a few years. I really believe we will be a really good team in the near future.’’

The Sox once again demonstrated the ‘‘near future’’ is a ways away. Shortstop Tim Anderson committed his 10th error and second baseman Yoan Moncada his fifth. Moncada also struck out for the eighth, ninth and 10th times in his last four games.

In the Indians’ five-run third, a liner by Melky Cabrera skipped past struggling right fielder Daniel Palka for a two-run double and left fielder Trayce Thompson and center fielder Adam Engel almost collided on a fly ball Thompson caught. Not a good look.

In between, right-hander Reynaldo Lopez — the Sox’ best pitcher and a key piece in their rebuild — was lifted after allowing seven runs and eight hits in 2 2/3 innings, his worst start of the season.

‘‘I don’t know how to explain it,’’ Lopez said through a translator. ‘‘I was feeling good and was feeling strong, and my pitches were good. Just sometimes you can’t explain it.’’

Abreu’s sizzling May came to an end with a hitless series. He’s batting .298 with nine homers, 19 doubles and 31 RBI.

The All-Star ballots were released Wednesday, with Abreu standing out among the Sox. Designated hitter Matt Davidson, who is injured, and Anderson are having good offensive years, too.

‘‘If I’m representing this team in the All-Star Game, I would be honored,’’ Abreu said. ‘‘But it’s not my focus right now. My focus is to help this team win games. If you take care of things you can do on the field, those things will take care of themselves.’’