CHICAGO -- There weren't many positive moments produced by the White Sox through the first three innings of Thursday's 7-6 loss to the Twins at Guaranteed Rate Field.

Minnesota scored the game's first six runs off Derek Holland, with four first-inning runs being unearned because of first baseman Jose Abreu's error on what would have been an inning-ending double-play. At the plate, the White Sox had no hits against Twins starter Phil Hughes through three.

Manager Rick Renteria's crew didn't give up, though, finishing one run short.

"When we got to the point where we were at in that ballgame ... I'm sure everybody thought it was all over," Renteria said. "It certainly wasn't, because they ended up having to bring in their closer for a five-out save. That says something for our club."

Brandon Kintzler recorded the first five-out save of his career for the Twins, having to strand runners on second and third in the eighth by striking out Omar Narvaez and Leury Garcia. The White Sox did make matters interesting behind a three-run homer from Melky Cabrera, Matt Davidson's solo shot and four innings of hitless relief from Anthony Swarzak, Dan Jennings, Tommy Kahnle and Player Page for David Robertson, including the last six outs coming via strikeout.

"That's kind of what you ask for from our team every night," Davidson said. "We want to come out on top, but we want to give every team a fight and [have them] know we're not backing down."

"It was huge," Holland said of the comeback. "No matter what, we didn't give in. That's what it's all about. I put us in a hole. The offense came up big. We didn't get what we wanted, the final result, but that shows a lot of heart from this team."

Holland acknowledged that the club needs to stay the course during this rough patch, having lost five straight -- its longest skid since dropping six in a row from Sept. 17-23, 2016. The White Sox have been limited to 15 runs over the five losses, going 5-for-31 with runners in scoring position and stranding 38 baserunners.

These moral victories might outnumber actual victories by the time the season is over for a rebuilding White Sox club. They have played better than everyone outside of the clubhouse expected at the start of this season, but their look could change drastically as the non-waiver Trade Deadline approaches.

General manager Rick Hahn has spoken about tough stretches the franchise will have to endure as part of the rebuild, but he also has talked about doing things the right way on the field, even in defeat.

• Hahn: White Sox being patient on trade front

Thursday's effort wasn't perfect, but a somewhat feisty Renteria stood behind his group's will and focus even after the rough start.

"Well, it wasn't as deflating as you might think, because we kept fighting," Renteria said of the Abreu error. "We came within one toward the end. It wasn't deflating enough. It was just not a good start, to say the least. But that being said, I thought, 'For goodness sake, we got those guys out there continuing to battle, chip away.'"