The 19-year-old, ranked 144 in the world, said he got all fired up by his Malaysian mother Norlaila thinking he had no chance against the two-time Wimbledon champion.
"I was reading a comment that she thought Rafa was too good for me. It actually made me a bit angry. You would think he's in a whole other level compared to me. I just believed in myself that I could create some opportunities," the Australian said.
"I'm pretty happy. That's the biggest win of my career, and that's something I'm never going to forget. I'm going to draw so much confidence out of that no matter where I play now. To have that under my belt, it's massive," he said.
The wildcard performed a victory jig on the Centre Court, a dance move he called the "juicy wiggle".
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The teenager did not have time to speak to his mum on the telephone but said: "I'll just text her a smiley face."
Kyrgios next faces the huge-serving Canadian eighth seed Milos Raonic on Court One on Wednesday for a place in the semi-finals.
"I'm just a normal kid, 19-year-old. I play a lot of Xbox. I brought my Xbox with me. Never did I think a week ago I was going to make the quarter-finals of Wimbledon in my first appearance," he said.
"At that stage you just think about all the work you put in. You know if you believe in yourself. Especially with my serve, if I just go after it, hit the right spots, I'm going to have a pretty good shot to close out a match.