It didn't pan out, as the Royals' offense, the worst in baseball, was shut out, including mustering just four hits in eight innings against Quintana.
Cuthbert, Colon and Butera combined to go 1-for-9, the one hit being a bunt single by Colon.
"It is tough to get them in games," Yost said. "When you're struggling offensively like we are, it's hard to get them [at-bats], especially when they're not producing, either. It's not their fault, because they're not getting playing time."
Yost sat left-handed hitters Mike Moustakas, Alex Gordon and Brandon Moss.
Moustakas (.286 batting average, three homers, six RBIs) and Gordon (.288, two homers, five RBIs) have decent career numbers against Quintana. But Moustakas didn't see the ball well last week against Quintana.
"Four punchouts," Yost noted.
Moss is 0-for-5 in his career against Quintana and is hitting just .159 this season.
Cuthbert hit two home runs off Quintana last season, but is now 0-for-6 this season against the lefty, striking out four times.
Yost obviously is searching for anything to jump-start an offense that has been cold all season.
"And while Quintana has been tough against us, we have found ways to beat him," said Yost, whose team is 9-3 against the White Sox starter. "He was really good. Give him some credit. He made the All-Star team for a reason."
Royals utility man Whit Merrifield said it's just a matter of an offense that keeps struggling, no matter who is in the lineup.
"The way to beat [Quintana] is capitalize on mistakes," Merrifield said. "He was good tonight, but he still made mistakes. When you're going good, you capitalize on mistakes. When you're not, you pop pitches up."