The Indians scored just 13 runs in the six games and compiled a .183 batting average.
"It was a really tough trip. There's no way around it," manager Terry Francona said. "Not a lot went right for us. But we have to put it behind us. We have to go fix it, and we'll do that."
The status of Jason Kipnis is in doubt after he was held out of Wednesday's loss to the Los Angeles Angels of Anaheim with a strained abdominal muscle. Francona said he might be placed on the disabled list, depending on how he feels.
"We've all seen it and been around it - where during the action of a game, a guy feels like it's minimal," Francona said. "Then they wake up in the morning and feel like they've got a knife stuck in them. He doesn't feel like that, so that's good."
The White Sox have lost six in a row in Cleveland and were 1-8 there last season. They'd lost 14 straight against the Indians until winning three of four in Chicago last month.
Lefty John Danks starts for the visitors in a second straight matchup against Cleveland's Danny Salazar, whom he beat in the opener of the April series.
Danks allowed three runs in six innings in that 7-3 triumph and is 3-1 with a 2.79 earned run average in his last six starts at the Indians' home.
Cleveland is 3-8 in 2014 against lefties.
Salazar was nicked for five runs in 3 2/3 innings in the loss to Danks, which started an ugly stretch of three straight losses in which he allowed five runs and didn't last past five innings.
The streak ended in non-winning style in his last start on Sunday, when he gave a single run in seven innings of the Indians' 4-1 loss in San Francisco.
On Wednesday in Chicago, Bryan Holaday's two-run double fueled a four-run fourth inning as the Detroit Tigers defeated the White Sox, 5-1.
Dayan Viciedo went 2-for-4 with two doubles and a run scored. Tyler Flowers' single drove in Chicago's only run.
Hector Noesi (0-2) lasted just 3 2/3 innings and allowed four runs on five hits.
In Anaheim, Hank Conger hit a two-run home run and the Angels beat the Indians, 7-1, to complete a three-game sweep.
David Murphy drove in the only run for the Indians. Elliot Johnson had a double for Cleveland's only extra-base hit in the game.
Indians starter Zach McAllister (3-2) gave up five runs -- four earned -- on four hits while striking out five and walking four over 4 1/3 innings. McAllister had a streak of 37 homerless innings snapped by Conger in the second.
"Zach competed but it was hard for him," Francona said. "His line was worse than how he pitched."