The British socialite - who was often babysat by the legendary artist at his Factory studio after her parents, Sir Mick Jagger and Bianca Jagger, divorced - explained the American pop artist was so taken with the effect created by the mishap, he asked her to do it again.
She explained: "I spent a lot of time during the day at Andy's. I had my first glass of champagne with him. No wonder I peed on his photo base paper once! But he didn't freak out, he liked the effect and later asked me to do it again."
"I think that I was lucky: my mother was always surrounded by artists who then inspired me in my posterior artwork."
The 38-year-old designer believes she inherited her "bravado" from her Rolling Stones singer father and her "stubborn" attitude from her actress mother.
She added to German magazine Gala: "If there is one thing I inherited from my father, it is to say what I think. I am not afraid to offend anyone. Admittedly, I also inherited his bravado - but showing-off is something I only do at home.
"From my mother I inherited her stubbornness. She has always been opinionated, she is a strong woman. My mother always fought for what she believed in."