"It's a combination of both," Guillen said. "He pitched good and we're not swinging the bat well. We're struggling at the plate, big time."
One change Guillen might make is dropping designated hitter Adam Dunn, who missed six games after having an emergency appendectomy on April 6, down in the lineup from his current third spot. Dunn went 0 for 4 on Tuesday night, including three strikeouts, and has two hits in his last 27 at-bats.
"Just so he can relax," Guillen said. "When you're out for a few days, it takes you a little while to come back and regroup."
"He threw the ball pretty good," Guillen said. "Threw a lot of strikes. A nice combination of breaking balls, cutters."
Danks (0-2) gave up two runs and seven hits in seven innings for the White Sox, who have lost six in a row. The left-hander struck out five and hit two batters.
Guillen said the offensive struggles make it harder for the pitchers.
"They make one mistake, they could lose the game," Guillen said. "You have to make every pitch count. You can not have the luxury to make a bad pitch. Obviously, you put more pressure on them."
Danks held the Rays without a hit in six at-bats — including a pair of strikeouts by B.J. Upton — with runners in scoring position through three innings, and 0 for 8 overall.
"Our job is to go out there and give them a chance," Danks said.
The White Sox, who have scored just 29 runs over the last 10 games, tied it at 1 on the fifth. Carlos Quentin hit a leadoff double and scored on A.J. Pierzynski's one-out single to center.
The Rays went back in front in the bottom half on Sean Rodriguez's run-scoring triple.
Shields ended the game by striking out Dunn and Konerko with Juan Pierre on second.
"I definitely needed to battle through those two guys," Shields said. "They're some of the best hitters in the league and I made some decent pitches on them."
NOTES: Tampa Bay LF Sam Fuld, the replacement for All-Star Carl Crawford, received high praise from Rays manager Joe Maddon. "There's no drop off," Maddon said. "Sam's playing that level of defense right now. All the different things he's doing defensively, I can't say that Carl's better." Crawford signed with Boston during the offseason. ... Danks didn't allow a run in the first three innings of his other three starts this season. ... Danks hit two batters in a game for the first time.