He didn't. Instead, he pointed straight to Greinke, who improved to 6-0, lowered his ERA to a Major League-best 0.40 and helped extend the White Sox losing skid to three games.
"To me, he's the best in the league right now," Guillen said.
It would be hard to argue with that. The White Sox accumulated six hits as Greinke baffled them with a steady dose of 97-mph fastballs, biting sliders and slow looping curveballs.
"That's the best performance I've seen in a long time by any Major League pitcher," said Guillen, who compared Greinke's performance to former Royal Bret Saberhagen's no-hitter against Guillen's White Sox in 1991.
Greinke was so dominating, in fact, that he overshadowed a serviceable outing from Chicago starter Bartolo Colon.
Colon, who had won eight of his last 10 outings against the Royals, held Kansas City mostly in check, but a high pitch count forced him to exit after five innings. Colon allowed three runs -- two earned -- on seven hits and struck out seven.
"Colon was good," Guillen said. "He was really good. He just competed against the wrong guy."
And it seems the White Sox batters did, too.
Chicago didn't have a runner in scoring position until the seventh inning and didn't mount a serious scoring threat until the eighth.
Trailing, 3-0, Paul Konerko singled to center to lead off the eighth inning. A.J. Pierzynski followed with a bloop single that dropped between the shortstop and center fielder. But Greinke got Scott Podsednik to ground into a double play and then struck out pinch-hitter Wilson Betemit, who was batting for Brent Lillibridge, to end the inning.
"There's no question he's as good as there is right now," said Konerko, who finished 0-for-3 but hit the hardest ball of the day off Greinke when he lined out to center field in the fifth.
"He's just got the command going right now. He's got the feel going," Konerko added. "Any time you have a power pitcher that gets that feel for throwing quality strikes -- not just right down the middle -- he's gonna be tough."
The Royals didn't need much offense, but they capitalized on a misplayed ball by right fielder Podsednik to take a 1-0 lead in the second inning. With runners at first and second and one out, Alberto Callaspo singled to right. Podsednik was unable to field it cleanly, and Jose Guillen scored from second base.
That would be all the Royals would need, though they added two more runs in the third inning behind a home run from David DeJesus and an RBI single from Billy Butler.
Greinke did the rest, clamping down on the White Sox for nine innings and notching his second shutout of the season. Greinke, who tied a season high with 10 strikeouts, struck out every White Sox starter except Podsednik, who finished 2-for-3. Pierzynski also added two hits in three at-bats.
"Definitely my favorite game of the year so far, if not ever," Greinke said. "That was a lot of fun."
Of course, it wasn't so much fun in the White Sox clubhouse. Dye and Fields still were hurting, Chicago lost for the fourth time in six games, and to make matters worse, the Sox dropped 2 1/2 games behind the surprising first-place Royals.
But this night belonged to Greinke, and Guillen and the rest of the White Sox had no answers for Kansas City's undefeated ace.
"It doesn't surprise me what he's doing right now at all," Guillen said, "because he's that good. He's been good for a long time. Now, he believes in himself."
Konerko put it a little more bluntly.
"Sometimes you avoid guys like that," Konerko said. "Sometimes you go right into the buzz saw."