"Zack Greinke at his April best probably isn't good enough Friday to overcome the Royals' white-flag attack. And he was far from his April best.

Not bad, really. Just not April.

And not nearly good enough to halt the Royals' free fall, which accelerated further in a 5-0 loss to the Chicago White Sox in front of a fireworks-fueled sellout crowd at Kauffman Stadium.

The chief problem, as usual, was the Royals' inability to mount an attack, although there was also a costly error by second baseman Alberto Callaspo that led to two unearned runs.

"It wears on you," manager Trey Hillman said. "We've got to have better at-bats with the consistency one through nine _ especially one through six with guys who have some sort of history.

"They're not living up to that history. We've got to get more production out of guys who have shown a history of doing it."

The Royals suffered their sixth shutout of the season. It also marked their fourth straight game of scoring fewer than two runs, which ties a franchise record for futility. It happened twice in 2004 and once in 1984, 1974 and 1970.

"I know I missed a couple of pitches," catcher Miguel Olivo said. "I don't know…you just come out and play (today)."

The Royals did little against Chicago starter John Danks, 7-6, before loading the bases with one out in the eighth inning. That threat fizzled with reliever Scott Linebrink got Callaspo to ground into a double play.

Linebrink then closed out Chicago's seventh straight victory.

"We're finally playing up to our capabilities," said Danks, who allowed just five hits in 7 1/3 innings. "We've been saying we're better than what we've shown, and this last week or so we've started to prove it."

The White Sox got the only run they needed on A.J. Pierzynski's one-out homer in the second inning. The two unearned runs came in the third inning before Chicago added single runs in the fourth and seventh.

Greinke, 10-4, lasted just six innings before exiting after yielding four runs and nine hits. Two runs were unearned, which enabled him to record his 14th quality start in 17 outings.

"Not one of my best," he said. "It was mainly just a couple of guys who always beat me, and they did it again -- (Scott) Podsednik and Pierzynski. I just can't get those two out. I've thrown everything, and they've hit everything.""