"It can't happen," Upton said, "especially in the middle of a pennant race. Every run matters, every out matters, so I want to apologize for it. It's just something that can't happen."
The 23-year-old Upton has been benched twice this month for a lack of hustle, and although Rays manager Joe Maddon called Monday's scenario more "assumption" than lack of effort, the instance still caused a stir.
In the fourth inning of Monday's win, Upton was tagged out from behind by Angels first baseman Mark Teixeira while coasting into an unguarded second base.
Following the play, Upton was booed by the home crowd at Tropicana Field.
Veteran Cliff Floyd was among those in the Rays' clubhouse after the game who wanted to eradicate the behavior.
"You've got a guy who, in my opinion, is going to be different," Floyd said. "I'm going to put my butt on the line by saying that. I'm going to do everything possible, and I think everybody in here is going to do everything possible to make sure it doesn't happen again. It's not in Joe's hands anymore. It's not in anybody else's hands but ours as players."
Upton admitted he wasn't ready to address the situation with the media following Monday's game, but did speak with teammate Carlos Pena.
"I don't think people should be quick to judge B.J.," Pena said. The Rays first baseman said he called Upton late Monday night to talk baseball and give some "brotherly love" to his teammate.
"So what? There's been a couple of incidents that obviously shouldn't have happened," Pena said. "He knows it. I know it. And like I said yesterday, no one feels worse than him when things like that happen."
While no disciplinary action was taken following Monday's game, Maddon was pleased that the issue had been handled internally by some of the veteran players.
"It's the way it should be," Maddon said. "And it's how these things should be handled. I really want to move beyond all this. The focus needs to be on how well we are playing and the accomplishments of these guys in [Monday's] game."
And certainly no one is more eager to move on than Upton himself.
"The last thing I want to become is a distraction to this team," Upton said. "We've got something way too good going on right now to have to deal with this. I think we just want to win ballgames, and right now, I think I'm becoming a distraction. So I just can't let it happen, for my sake and for the team's sake, so we can move on and get to where we need to be."
As for how the string of incidents may be perceived, Upton wasn't worried about being saddled with a negative reputation.
"I know that's not me," he said. "I feel like I go out and play hard every day. I want to win as much as anybody in this room. Once again, things like that can't happen. It just so happens they're magnified a little bit more now than they have been in the past. So it's something I've got to deal with and not let it happen again."
Brittany Ghiroli is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.