The animated Perez angered Kansas City's Jarrod Dyson for a gesture he made after striking out the Royals outfielder in the ninth inning of Cleveland's 8-5 win on Monday.
After fanning Dyson on three pitches, Perez walked off the mound and waved his hand in front of his face to mock Dyson, who was unaware of the gesture until seeing it later on videotape.
"It's just terrible," Dyson said. "Nobody told me about it. As soon as I got done with my at-bat, I went down to see where the pitch was because I felt like the pitch was in and I saw him do that and it (ticked) me off even more."
It's the latest incident involving Perez, who recently criticized Indians fans for their lack of support and was fined earlier this season by Major League Baseball for an inappropriate tweet after the teams had a contentious series in Kansas City.
Perez said teammate Tony Sipp, who is friends with Dyson, had told him the Royals weren't happy with some of the comments and they were "coming for me."
During Monday's game, Perez promised his teammates in the bullpen that if he struck out Dyson he would make the "you can't see me" gesture popularized by pro wrestler John Cena.
Perez said before Tuesday's game that the gesture was in response to what Dyson told Sipp.
"That's the only reason I did it," Perez said. "I said, 'All right, you're coming for me, I'm coming for you. If I strike you out, you're going to get the can't see me face.'
"What happened? Three pitches. You can't see me," he said.
Dyson said he was already looking forward to his next matchup against Perez, who leads the majors with 17 saves.
"I can't wait to face him again," Dyson said. "I want to beat him. That's the good part of this game, you get to go back and try to beat a guy, beat a team. If I had seen it, I would have said something, probably jumped out of character. Usually, that's not me. Though that's not how our organization is.
"But that's the game. When you win, you can say what you want," Dyson added. "They beat us. We lost. We have nothing to say. You lose, you shut up and go out and try to beat them. Then you can have something to say."
Perez wasn't troubled that Dyson didn't appreciate his actions.
"If he took offense to it, oh well," Perez said. "It happened and it's the same as when a hitter hits a home run and they come back to the dugout and do all their hand-slapping stuff. We see that as pitchers and we don't take offense to it because he just hit a home run."
Dyson chalked up Perez's antics to "him just being him."
"I think that's just the way he is. That's just him. If he needs that to get motivated, whatever. It was a little bit of disrespect," Dyson said. "I guess he felt good striking me out. It's not like he struck out Albert Pujols."
Perez has been known to let loose with a primal scream after getting a save or pumping his fists in celebration. While it may annoy and even anger some of his opponents, the rebellious right-hander said he does it to motivate himself.
"(Winning) definitely gives me some leeway to do what I do," he said. "Nobody wants to hear this from a last-place team. I mean, who cares, you're in last place. You talk the talk, you have to walk the walk. We're in first place right now, and it's fun. I know that, if I'm blowing saves, I can't do that stuff, either.
"I'm enjoying this. This is fun," Perez continued. "It's not very often you can go on a streak like this, especially in the big leagues, and pitch as well as I have been. Not trying to pump myself up, but it's fun."