Cori Gauff says it is the "first time I have ever cried after winning a match" and "wouldn't be here" without Williams.
Former Wimbledon champion Venus Williams has been beaten by a 15-year-old qualifier in one of the tournament's greatest ever upsets.
American Cori Gauff - the youngest player to qualify for Wimbledon in the Open era - overcame her famous opponent 6-4 6-4 on Court One.
Williams won four Grand Slams - including two Wimbledon titles - before Gauff was born, and has five Wimbledon titles in total.
Gauff said Williams was "so inspiring" and that she "wouldn't be here if it wasn't for her".
Asked about the teenager's future, Williams said "the sky's the limit".
Despite not showing many nerves, Gauff said she had to "remind myself that the lines are the same lines, the courts are the same size", she told the BBC.
After every point, she urged herself to "stay calm".
When she won she dropped her racket, held her head in her hands, and looked tearful.
It was the "first time I have ever cried after winning a match" and "didn't really know how to feel", she said.
Gauff, who was born in Atlanta and lives in Florida, added: "I never thought this would happen. I'm literally living my dream right now. Not many people get to say that."
Gauff made only eight unforced errors, compared to Williams's 25, and her serve was broken only once.
She also struck more winners - 18 compared to 16.
At 39, Williams is 24 years Gauff's senior, and 269 ranking spots above her.
But the youngster played fearlessly and a break of serve in the fifth game of the opening set was enough to win it.
The apparently nerveless display continued into the second set, Williams netting a forehand on Gauff's fourth match point.
Gauff said Williams was gracious in defeat: "She told me congratulations and keep going, she said good luck and I told her thanks for everything she did.
"I wouldn't be here if it wasn't for her - I told her she was so inspiring and I've always wanted to tell her that but I've never had the guts to before."
"She [Venus Williams] said congratulations."— Wimbledon (@Wimbledon) July 1, 2019
"I told her thank you for everything that you did. I wouldn’t be here without you. I always wanted to tell her that."
- @CocoGauff #Wimbledon pic.twitter.com/lGUYiGnq3Q