CHICAGO -- Dylan Cease was not satisfied.

The rookie had just finished the first quality start of his young career in the White Sox 6-2 loss to the Astros in Game 1 of Tuesday's doubleheader at Guaranteed Rate Field. He allowed four runs, but only two of them were earned, in six-plus innings against one of the best teams in the game.

• Box score

But he also issued four unintentional walks and allowed two solo home runs, bringing his season total to eight long balls in seven starts, leaving him wanting more after the White Sox fell to 1-3 on this six-game homestand.

“I didn't execute pitches that great, but we had a chance to win, so that was OK. But I mean, it's hard to be happy with a loss,” Cease said. “Just across the board. I didn't feel like my offspeed was that sharp today, and I didn't feel like I had great fastball command.

“Yeah, I'm definitely not discouraged. Just the end result like that, it is hard to be happy.”

A big inning had plagued Cease in each of his previous six trips to the mound, whether it was based on runs scored and elevated pitch count or both. Cease avoided that problem on Tuesday, but there certainly could have been an issue right from the start.

George Springer hit the first pitch he saw from Cease for a 467-foot home run, followed by Jose Altuve’s infield single and Michael Brantley’s bloop double to left. Cease came back quickly to retire Carlos Correa on a popout to second, and after an intentional walk to Yordan Alvarez loaded the bases, Yuri Gurriel hit into an inning-ending double play.

Manager Rick Renteria knew of Alvarez’s unreal run of late, just as he knew about Gurriel’s great season. He decided even in the first to take his chances with righty on righty in Cease vs. Gurriel via the Alvarez free pass.

“To Dylan’s credit, he made a nice pitch to induce the ground ball,” Renteria said. “[Pitching coach Don Cooper] was saying, 'It’s a lot of confidence you showed when you walked to load the bases in the first.' I have confidence in Dylan Cease, and he made a good pitch to get out of that inning. He’s got good stuff.”

Cease threw only 15 pitches in the first and limited the damage. He gave up a leadoff homer in the third to Altuve but retired the next 11 in a row, including eight via the ground ball. In one stretch, from the fourth to the fifth, Cease retired five straight on nine pitches.

Houston scored the go-ahead run in the sixth when Alvarez raced home from third on a Welington Castillo passed ball. Renteria challenged the call, as it looked as though Cease's glove might have gotten Alvarez’s foot before the foot hit the plate, but the call stood. The Astros added a run in the seventh on a second Castillo passed ball, scoring in that frame without benefit of a hit.

In addition to allowing the three passed balls, Castillo was thrown out at the plate to end the second on a Matt Skole single to right against Houston starter Zack Greinke. Springer made a 96.3-mph throw from 238 feet, per Statcast, to get the out.

Tuesday’s outing marked another step forward in the learning process for Cease, even if he didn’t like his execution.

“For me, at the end of the day, it's how I execute pitches, and I didn't feel like I did it great today,” said Cease, who topped out at 98.6 mph, per Statcast. “I always judge my outings on that, not necessarily the results, because those can be misleading.”

“I said to our guys before the game, I thought [Cease] was better than his numbers indicated,” Houston manager AJ Hinch said. “He's had a couple of blow-up innings that have gotten him, but he's got a good arm and good stuff. We knew we're going to get some fastballs to hit. He threw his breaking ball a little bit, and I thought he did a nice job of hanging in there. He's got a nice, young arm.”