The right-hander's one mistake came against White Sox first baseman Jose Abreu, who hit a two-run home run over the right-field fence for the first runs of the game in the sixth inning.
Graveman felt he was making incremental improvements in each of his spring appearances, and that carried over into the regular season. He threw all of his pitches for strikes and blamed himself for losing concentration in the sixth.
"I needed to stay focused after the four-pitch walk and not let a pitch drift back over the plate," Graveman said. "I need to make pitches down in the zone and not elevate to a good hitter."
A's catcher Stephen Vogt said Graveman is showing all the signs of a mature pitcher.
"He has grown up a lot," Vogt said. "He learned a lot last year and is continuing to learn. He has a lot of confidence in what he throws, and that's a sign of maturity."
Graveman, who said he lost 12 pounds during his illness, said he had enough stamina to continue pitching.
"The training staff did a great job getting me prepared for the game," he said. "I felt good going in. I think it was just a bad pitch."
Graveman was not helped by his offense, which didn't score its lone run until Chris Coghlan's RBI single in the ninth after the White Sox pulled away with four runs in the top half.
"I thought he was outstanding," Vogt said of Graveman. "The last inning was tough with the walk and home run, but he gave us a chance to win. We need to be better for Kendall when he's doing that well."
Vogt thinks it's only a matter of time before the A's offense starts producing at a higher level.
"This team is going to hit. We ran into four very good pitchers," Vogt said. "We hit all the way through spring, and we'll catch our stride."
"I expect us to come around," Melvin said. "We have guys with track records."
Rick Eymer is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.