The benching was the first of the postseason for Swisher, who is 4-for-26 in seven playoff games. Rodriguez sat for the second time, having also been on the bench for the deciding Game 5 of the AL Division Series against the Orioles. Girardi has pinch-hit for Rodriguez in three other games.
"We're just trying to find a lineup that works," Swisher said after Game 3. "I thought it was a great lineup. I wasn't in it, but you've got to back your guys and support your teammates. The guys played well; we just came up a little short."
Swisher was on deck to pinch-hit for Russell Martin when Raul Ibanez struck out to end the game against Detroit lefty Phil Coke. Girardi said he didn't consider using Rodriguez to pinch-hit for Ibanez against the lefty because the Tigers would have then brought in right-hander Joaquin Benoit.
"Ibanez has been one of our best hitters down the stretch here," Girardi said.
Girardi said that if he had to choose between keeping a healthy relationship with a player or winning a game, he would always pick winning. But he knows he may be losing some of his players, particularly Rodriguez, who remains under contract through 2017.
"Of course that's something that you have to worry about, but I don't think you can really worry about it today," Girardi said. "Relationships go through their up and down periods, no matter who you are, and you have a chance to rebuild them."
Girardi also said that his decision to not start Rodriguez was strictly related to performance and had nothing to do with Tuesday's report in the New York Post that said Rodriguez was interacting with female fans behind the Yankees' dugout in Game 1.
During the season, Girardi often defended lineup choices by saying that he believed in his players' track records. But now, with the Yankees facing elimination, he's working with a much shorter leash, recognizing that such moves could come at a cost in the future.
"At the end of the day, we have to put all that stuff aside and try to put our best foot forward every single day -- regardless of hurting feelings or not," general manager Brian Cashman said. "That stuff will play itself out, one way or the other. I can't predict it, but I respect it if someone is upset. I have no problem with that."