Rays manager Joe Maddon took the one-game action, saying the topic of running hard on grounders was discussed at a team meeting in Kansas City two weeks ago.
Asked about the benching, Upton said: "I just work here."
Cleveland designated hitter Ryan Garko got an early exit, too, in Wednesday's game after failing to run.
Garko stood in the batter's box when his squibber down the first-base line stayed fair in the second inning. Andy Marte pinch-hit for Garko the next inning.
On Tuesday night, Upton hit a comebacker to Edward Mujica during Tampa Bay's 8-4 win. The pitcher bobbled the ball and went down to his knees before easily throwing out Upton at first base.
"I'm not happy with him not running out the last groundball last night," Maddon said before Wednesday's game. "I didn't take him out of the game ... everybody was hurt last night. So, I had to wait until today to do it."
The AL East-leading Rays were without left fielder Carl Crawford (sore left hamstring) and shortstop Jason Bartlett (right index finger) on Tuesday. Also, utilityman Willy Aybar experienced hamstring cramping in Monday's game, and catcher Shawn Riggans had soreness in his chest, the result of being hit by a pitch on Sunday.
"I really don't believe in a whole lot of rules and regulations," Maddon said. "Personally I don't believe in it. I like to believe that you are a man and can pretty much police yourself."
Ben Zobrist replaced Upton in center field, while Aybar started at short.
Bartlett, who missed the previous two games, was the designated hitter. It has not been determined if Bartlett, who threw before the game, will play in the field Thursday.
Crawford was out of the lineup for third straight day. He might return Thursday.
"I hope so. I'm definitely ready to get going," Crawford said. "It's better. Still like a little strain in there. Still tugs when I raise my leg. I'll have to be careful with that. I think I know how to manage it the way I want."