"It's stuff that happens in the game," Cordero said. "Unfortunately, it happened tonight. We get the loss, but we won two out of three, so we just have to do that every time, try to win two out of three, and we'll be OK.
"But next time, if I have men in that position, I just have to make a better pitch. I have to make a pitch if you want to get people out in the big leagues."
The ninth-inning numbers have not been very kind to Cordero this season. With the season just over two months old, the sample size is small, but Cordero has surrendered all but one of his 15 earned runs in the ninth.
Cordero has allowed just one run in 12 2/3 innings when pitching in the seventh, eighth, or in extra-innings. In the ninth, though, he has allowed 14 runs in just 10 2/3 frames.
Most of that damage came during a span when he was filling in for injured closer Sergio Santos. In fact, since losing that role on May 8, Cordero has allowed just three runs in 12 innings, but one of those came in untimely fashion on Thursday night.
Cordero's problems against the White Sox began when he surrendered a one-out single to Dayan Viciedo. Chicago's left fielder then advanced to second on a wild pitch which got away from catcher J.P. Arencibia to put himself in scoring position. Hudson came through two batters later with a sharp single on a 1-1 fastball.
"It's not the first time it's going to happen, it's not the last time it's going to happen," Cordero said of the changeup in the dirt that got away. "You just have to make a pitch. ... Unfortunately I left the pitch a little bit up, and [Hudson] got a base hit and they won.
"I know J.P. didn't want to do that, and I don't want to throw that pitch up there. It's going to happen. You just have to make a better pitch."
The ninth inning overshadowed a relatively strong outing by Blue Jays right-hander Henderson Alvarez. The native of Venezuela surrendered one run in the first before settling down and cruising through most of his start. At one point between the first and fifth innings he retired 12 consecutive batters and appeared well on his way to a win.
That chance evaporated in the sixth when Alex Rios hit a two-run homer over the wall in left field to tie the game at 3. Rios' sixth home run of the season was the 13th Alvarez has surrendered in 12 starts this season.
Alvarez remained in the game through seven innings and was charged with three runs on seven hits while striking out two. The three runs were the least amount he has surrendered since May 10, which also was the last time he earned a victory.
"I'm happy with the way I pitched," Alvarez said through interpreter Luis Rivera. "I feel like all my pitches were working tonight, the sinker, the slider and the changeup. I was happy with that outing."
The Blue Jays scored three runs in the second inning on a two-run single by Mike McCoy and a throwing error by shortstop Alexei Ramirez. But from that point on, they were shut down by Chicago's pitching staff.
Right-hander Jake Peavy allowed just those three runs -- two earned -- on four hits while walking five and striking out four. It's not that the Blue Jays didn't have chances, they just didn't come through when the opportunities presented themselves.
Toronto managed to go just 1-for-11 with runners in scoring position while stranding 10 men on base en route to having its three-game winning streak snapped.
"After losing the first two, you have to salvage a game," Peavy said. "Seemed like they caught every break -- ball bounced their way all night. The boys just battled. That's the M.O. of this team. It could have got ugly early, but it was a great team win."
The Blue Jays' six-game road trip will continue on Friday with a three-game set in Atlanta. It wasn't the desired outcome in Chicago, but the club is still able to settle for its sixth consecutive series win over the White Sox.
"To win a road series is always a good thing, but we set ourselves up for a potential sweep here, but they didn't roll over by any means, and we were in a tight game all the way to the end," Blue Jays manager John Farrell said.