CHICAGO -- What little hope remained for the Indians to catch the Twins in the American League Central was abolished on Wednesday night as Minnesota clinched the division. With just four regular-season games remaining, the Tribe knows it has no room left for error in order to make the postseason.

After topping the division for the past three years, the Indians are now left to solely focus on finding a way to secure a spot in the AL Wild Card Game after an 8-3 loss to the White Sox at Guaranteed Rate Field allowed the Twins to pop champagne in their clubhouse in Detroit.

“At the end of the day, we just got to finish one game better than now two teams,” shortstop Francisco Lindor said. “Before, it was three teams. Now, it’s two teams. Congrats to Minnesota. Let’s try to go get the Wild Card.”

• Box score

The performance on Wednesday was far from what Cleveland needed in order to gain ground on its goal. Starter Shane Bieber gave up five runs (three earned) on 10 hits over 5 2/3 innings, the bullpen was charged with three more runs and Cleveland’s top five hitters went a combined 0-for-20 to fall 1 1/2 games back of Tampa Bay for the second AL Wild Card. The Indians are two games behind the A's for the top Wild Card spot in the AL.

“For not having a lot of hits, we had opportunities,” Indians manager Terry Francona said of his club, which was 1-for-6 with runners in scoring position. “They really did a good job on the top of our order. The first five guys didn’t get a hit. That’s a tough way to play.”

• Wild Card standings

The Tribe was within striking distance through 6 1/2 innings against the White Sox, trailing by two runs after José Ramírez’s solo home run in a two-run fifth inning. But the wind was knocked out of the Indians in the seventh when Tyler Clippard was called upon with one out and runners on the corners and gave up a three-run homer to Welington Castillo.

“The whole entire game, I felt like we were going to come back and win,” Lindor said. “I never really lost faith. We’ve got a good team. I thought we were going to come back and win the ballgame, but we didn’t. We didn’t execute it when we had to. I didn’t. I had a chance to tie the game or take the lead a couple times, and I didn’t do it.”

Lindor had two opportunities with runners in scoring position. The first came in the seventh inning with runners on first and second, and the Tribe’s leadoff hitter struck out swinging. Then, with two outs and the bases loaded in the ninth, Lindor was fanned for the third time on the night. In 106 at-bats with runners in scoring position this season, the 25-year-old has hit .208 with two homers, 35 RBIs, 20 strikeouts and a .625 OPS.

“I’ve been trying to do the same thing,” Lindor said. “It don’t matter whenever I got someone on base or no one on base. I just try to get on base. That’s what you want to try to do, get a good pitch to hit. Usually, when there’s someone on base, they’re not throwing strikes to me, and I chased lately a lot. So, I just got to continue to get better and do a better job to help my team win on a daily basis, and that’s really what it comes down to.”

The Indians’ struggles against the White Sox have lasted all season. One of the biggest differences between the Indians and the Twins, who clinched the American League Central on Wednesday evening thanks to Cleveland’s loss, is their records against the 69-88 White Sox.

“They play us good, man. They really do,” Francona said entering the series. “I give [manager Rick Renteria] a lot of credit. They play hard, they always have. … There’s certain teams that match up against you better, but they’ve played us really tough all year, that’s for sure.”

Chicago clinched the season series over the Indians with Wednesday’s win, outdueling the Tribe in 10 of their 18 matchups this year with Thursday’s series finale remaining. Meanwhile, the Twins posted a 13-6 record against the White Sox this season.

Now, the Indians just have Thursday’s game against Chicago before a three-game set against the Nationals. The Rays have three games remaining against the Blue Jays, and the A’s have a four-game series left against the Mariners.

“We don’t have a lot of games left, but we have some very important games,” Bieber said. “Crazier things have happened. We have to come here tomorrow and prepare like any other game and see how the cards fall.”