The British star finally ended his lengthy saga with Wilder after inflicting a crushing knockout in the 11th round to retain his WBC heavyweight title in Las Vegas.
But Fury has accused Wilder of rejecting his words of respect when he went to the American's corner after the fight.
"I'm not going to make any excuses, Wilder is a top fighter," said Fury.
"He gave me a real run for my money tonight, and I always said I'm the best in the world and he's the second best.
"He's got no love for me, Deontay Wilder, because you know why, because I beat him three times.
"I'm a sportsman. I went over to him to show some love and respect and he didn't want to give it back. That's his problem."
Revealing their verbal exchange, Fury told BT Sport Box Office: "I just said well done and he said, 'I don't want to show any sportsmanship or respect.' I said, 'No problem.'
"Very surprised. Sore loser, an idiot.
"To be a top fighting man, you've got to show guts and respect, and he couldn't do it tonight, and that was it."
Fury had floored Wilder in the third round, but was dropped twice himself in the fourth, before he knocked down the Alabama man again in the 10th and then dramatically ended the fight.
"I've got to say thank you to my trainer Sugarhill, because if it wasn't for Sugar, America's own, Detroit's own, I wouldn't have got through that fight tonight," said Fury.
"He told me. He said, 'Get your jab working big dog, and throw that right hand down the middle. Only the big dogs pull it out late on in fights.'
"I said, 'Yes, I've got you,' and I went and pulled it out of the bag."
Fury preserved his 32-fight unbeaten record, strengthening his status as the division's leading champion after Anthony Joshua lost his WBA, IBF and WBO belts in last month's unanimous decision defeat by Oleksandr Usyk.
"I'm now the greatest heavyweight of my era, without a doubt," said Fury.
"No 1. Look what I've done.
"I've come to America my last six fights and fought the most devastating puncher in the history of our sport.
"Not once, not twice, but three times."