The Australian beat Nadal 3-6 7-6 7-6 in the last-16 in Acapulco and will now face Stan Wawrinka in the quarter-finals.
But Kyrgios was booed by the crowd for some of his antics during the match – including an underarm first serve – and Nadal, who was clearly fuming and barely shook his opponent’s hand, took aim at him afterwards.
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The Spaniard said: "He is a player who has ginormous talent.
"He could win Grand Slams and fight the top positions of the ranking, but there is a reason why he is where he is.
He lacks respect for the public, the rival and towards himself.
But Kyrgios hit back immediately in his own press conference, saying: “I’m different, Rafa’s different, he can focus on what he needs to do.
He doesn’t know the journey I’ve been through, he doesn’t know anything about me so I’m not going to listen at all.
“It’s the way I play, it’s the way he plays.
“He’s very slow between points. There’s a rule in the books that says you have to play at the speed of the server, Rafa has the speed every time.
“I’m not going to comment on his game, he has his game, I have my game."
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