Speaking to tennis writer Ben Rothenberg on the 'No Challenges Remaining' podcast, the 24-year-old also disparaged a number of other top professionals and fans who heckle him at his matches.
Kyrgios has had a tense relationship with Nadal, who accused him of "lacking respect for the public, the opponent and himself" after being beaten by the Australian at the Mexican Open in March.
World number 36 Kyrgios labelled the French Open champion "super salty" -- slang for someone who is aggressive or ill-humoured -- and only gracious after victory.
"When he wins, it’s fine. He won’t say anything bad, he’ll credit the opponent, ‘He was a great player’. But as soon as I beat him, it’s just like, ‘He has no respect for me, my fans and no respect to the game’," said Kyrgios.
"It’s not a good look for you, I feel. And then uncle Toni came out saying, 'He lacks education'. I’m like, 'Bra (brother), I did 12 years at school, you idiot.
"I’m very educated. I understand that you’re upset I beat your family again’."
Turning his sights on another of the game's modern greats, Kyrgios described Djokovic as "an unbelievable player" and "a champion of the sport" but said the Serb was too desperate to be admired like popular Swiss rival Roger Federer.
"I just feel like he has a sick obsession with wanting to be liked. He just wants to be like Roger," he said.
"For me personally -- I don’t care right now, I’ve come this far -- I feel like he just wants to be liked so much that I just can’t stand him.
"This whole celebration thing that he does after matches, it’s like so cringeworthy. It’s very cringeworthy."
Kyrgios devoted special attention to Spanish veteran Fernando Verdasco, calling him "the most arrogant person ever".
He spoke warmly of three-times Grand Slam champion Andy Murray but also said the Briton's head-to-head record against Djokovic -- 11-25 in matches and 2-5 in Grand Slam finals -- was "embarrassing".
He gave no apologies for hitting back at spectators who give him a hard time during matches.
"These guys show me no respect. None," he said.
"So why would I show you respect? For instance, when I’m taking matches, I don’t care that you paid for tickets. You guys treat me like crap anyway."
Kyrgios, who has thrilled fans with the purity of his tennis and alienated some by flouting the game's conventions, plays Norway's Casper Ruud in the second round of the Rome Masters later on Thursday.
He will then bid to surpass the quarter-finals of a Grand Slam for the first time at the May 26-June 9 French Open.
(Reporting by Ian Ransom, editing by Nick Mulvenney)
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