But Ventura, never one to make decisions based on a knee-jerk reaction, chose the wait-and-see approach.
"We'll talk about that later," Ventura said. "Right now we're trying to figure out how to win a game."
That winning formula has been tougher to come by on the road, with the White Sox (35-40) losing their third straight to the Twins (35-38) in this four-game set and sixth straight away from home overall. They also have lost seven straight within the American League Central, adding the Twins on to three defeats at home against the Royals and one at home against Max Scherzer and the Tigers.
Working behind a starter who consistently has trouble getting through five, as has been Rienzo's story in three of his last four starts, doesn't exactly help in breaking those losing ways.
Rienzo allowed four runs on seven hits over 4 1/3 innings, striking out three and walking two. Over his last five starts, Rienzo has yielded 35 hits over 22 1/3 innings, along with 11 walks.
And the big inning once again cost the right-hander. With the White Sox clinging to a 2-1 lead in the fifth, the Twins scored three and knocked Rienzo from the game. Rienzo has allowed three runs or more in a single inning on four occasions over his last five starts.
• May 25 vs. the Yankees, four in the second.
• June 6 at the Angels, five in the fourth
• June 15 vs. the Royals, three in the third
• Saturday at the Twins, three in the fifth.
It's not so much a lack of confidence when these innings go astray for Rienzo, although that good feeling has been tested. It's more about a lack of experience.
"One inning," Rienzo said. "I always have one inning."
"You're seeing [Kevin] Correia kind of do the same thing, get in the same situations, and work his way out of it," said Ventura of Minnesota's starting and winning pitcher on Saturday. "Probably a little bit cagier at being able to get himself out of it."
In that fateful fifth, Joe Mauer doubled home Danny Santana and Brian Dozier on a long drive to left. Kendrys Morales followed with a run-scoring single. Mauer made hard contact on a 3-2 cutter and it seemed to slice away from Alejandro De Aza, but it was still a tough play that could have been made.
"I hit it pretty good. I thought it had a chance to go," Mauer said. "It's nice to come through in those situations for your team."
"Coming off a lefty's bat, you have to be a really good outfielder to be able to make that play," Ventura said. "I see [De Aza] making a good effort, it just started cutting away from him."
Conor Gillaspie's triple and Jose Abreu's single off of the right-field wall scored the White Sox first run in the opening inning off Correia (4-8). They added a second run in the second when Gordon Beckham was hit by a pitch with the bases loaded. A Gillaspie groundout stranded the bases loaded in that frame, and the White Sox wasted a two-on, one-out situation in the third when Dayan Viciedo hit into a double play.
Adam Eaton's triple and Beckham's sacrifice fly scored one, and Paul Konerko's pinch-hit single and pinch-runner Leury Garcia's stolen base put the tying run on second in the ninth off of closer Glen Perkins. But Perkins picked up his 19th save by striking out Abreu and Adam Dunn, dropping the White Sox to a season-low five games .500.
"Throw the Royals series out. I think we just got beat that series. This one I feel like we're beating ourselves, especially offensively," Dunn said. "Obviously they're out there trying to make a living as well. But we've got to do better offensively, that's the bottom line."
Carroll served as a White Sox bright spot with 3 2/3 scoreless innings of relief, furthering his cause for a potential flip flop with Rienzo. Much like Ventura, neither pitcher was talking postgame about future changes.
"That is not my job. That is Ventura's job," said Rienzo of staying in the rotation. "I just throw."
"My job right now is to come out of the bullpen and get guys out and help our bullpen," said Carroll, who has a 1.83 ERA over 19 2/3 innings in relief. "I'm just trying to do that to the best of my ability."