Kyrgios beat Tsitsipas in four sets -- 6-7(2) 6-4 6-3 7-6(7) -- in an action-packed, controversial game on Court One but the pair continued the feud at their post-match press conferences.
Tsitsipas had been frustrated by Kyrgios' "constant bullying" from the other side of the net and had tried to hit his opponent with a shot during the fiery encounter.
Kyrgios, who was vocal throughout, was warned for swearing by the umpire and was left furious when Tsitsipas wasn't disqualified for firing a ball into the crowd out of frustration.
"Yeah, it's constant bullying, that's what he does. He bullies opponents. He was probably a bully at school himself. I don't like bullies," Tsitsipas told reporters after the match.
"I don't like people that put other people down. He has some good traits in his character, as well. But he also has a very evil side to him, which if it's exposed, it can really do a lot of harm and bad to the people around him."
Kyrgios, who has already caused headlines at Wimbledon for both his outbursts and audacious shots, laughed off his opponents comments, calling them "soft."
He had previously said he had huge respect for the Greek when interviewed on court immediately after the match.
"I don't know what to say. I'm not sure how I bullied him. He was the one hitting balls at me, he was the one that hit a spectator, he was the one that smacked it out of the stadium," Kyrgios told reporters after progressing to the round of 16.
"I did nothing towards Stefanos today that was disrespectful. I was not drilling him with balls. To come in here and say I bullied him, that's just soft. We're not cut from the same cloth. I go up against guys who are true competitors.
"I've got many friends in the locker room, just to let you know. I'm actually one of the most liked. I'm set. He's not liked. Let's just put that there."
Tsitsipas later apologized for firing a ball into the crowd and admitted to trying to hit Kyrgios with a body shot.
"I'm not used to playing this way," he said. "But I cannot just sit there, act like a robot and act like someone that is completely cold and ignorant.
"Because you're out there doing your job, and you have noise coming from the other side of the court for no absolute reason.
"Every single point that I played today I feel like there was something going on on the other side of the net.
"That's his way of manipulating the opponent and making you feel distracted, in a way. There is no other player that does this. I really hope all us players can come up with something and make this a cleaner version of our sport, have this kind of behavior not accepted, not allowed, not tolerated."
Kyrgios, who will play American Brandon Nakashima in the next round, said Tsitsipas should be more worried about finding a way to beat him.
"I would be pretty upset if I lost to someone two weeks in a row. Maybe he should figure out how to beat me a couple more times first," the Australian added.