"If we don't win, we won't have a good road trip," Guillen said.
Justin Miller earned his first major-league victory with a 5-2 decision over the Sox, giving the Blue Jays a series sweep and handing the Sox a season-high three-game losing streak.
Miller took advantage of a struggling Sox offense with seven strong innings, allowing seven hits, two runs and striking out seven.
"I don't think this kid, with all due respect, is a strikeout pitcher," Guillen said of Miller, who was making his third start of the season.
Miller had just eight strikeouts in his previous 11 innings pitched but he baffled the Sox.
"That guy was awesome," Sox first baseman Paul Konerko said. "His slider was the best I've seen in the big leagues."
Konerko struck out twice and hit into a double play against Miller. He didn't fare much better after Miller left, striking out against Kerry Ligtenberg to end the game.
"Sometimes you have to tip your hat" to the pitcher, Konerko said. "On the whole, we've seen some good pitching."
Esteban Loaiza took the loss, his second straight. He pitched a complete game, allowing nine hits and five earned runs.
"It's a shame to leave a guy that pitched the way he pitched empty," Guillen said of Loaiza's performance.
The Sox have become a pretty predictable team. Again Sunday they jumped out to a lead when Frank Thomas missed a grand slam by a couple of feet, settling for a two-run single in the third inning.
But Toronto came right back in the bottom of the third on a single by Howie Clark and a two-run homer from Frank Catalanotto.
"It was a [cut fastball] below the knees," Loaiza said. "It was a great pitch."
Catalanotto can hit just about anything against the Sox this season. He finished the season series 12-for-22.
Toronto took the lead for good in the fourth with two runs on three singles and a sacrifice fly and added the fifth run on a two-out, RBI single by Orlando Hudson, who had a two-out, two-run home run in Friday's opener.
Meanwhile, the Sox offense continued to slumber. The Sox are two games better than they were after 30 games last season, but the offense is starting to resemble the unit that took an extended hiatus last May.
"We're struggling right now," right fielder Magglio Ordonez said. "We're not putting anything together."
After Miller left the game, Jason Kershner and Ligtenberg added four more strikeouts with Ligtenberg striking out the side in ninth, despite giving up a one-out double to Carlos Lee.
Even when they got runners on base, the Sox were unable to make anything happen. Lee and Joe Crede were thrown out trying to steal and the Sox hit into two double plays.
"The only thing we did well today was pitch," Guillen said. And even Loaiza's outing won't be considered a quality start.
Loaiza lost two games on this road trip, allowing nine earned runs and 19 hits in 132/3 innings.
The Sox finished the trip 2-4 and return home to face the Baltimore Orioles on Tuesday before the Minnesota Twins come to town for what may be a litmus-test series when it comes to the AL Central race.
For the Sox to prove they are legitimate contenders, they'll have to start hitting the way they believe they can.
"We're going to hit," Ordonez said.