The award-winning musician spoke to Gayle King on CBS Mornings last week, where he admitted he had "goosebumps" through watching his "nervous" and "frightened" daughter face the crowds.
"I know her, I know how nervous she was, I know how frightened she was [ahead of the first show]" he revealed.
On Blue's unique life - where everyone knows who she is thanks to her famous mom and dad - Jay-Z said: "Blue's been born into this world that she didn't ask.
She's been born into a life she didn't ask for. So since she was born she's been in, like, scrutiny and public eye, and everyone having an opinion."
He said of Blue's decision to perform on stage: "She wanted to do it. She wanted to do it the first night, and we was like, 'OK, if this is something you wanna do, you can't just go out there.
"You gotta go work with the dancers, and go work. And she worked every day and watched her work hard."
Blue has an incredibly close bond with her parents, who have managed to keep a lot of her private life out of the spotlight, despite their enormous fame.
Jay gave Gayle a sweet insight into his father-daughter bond with his firstborn during the two-part interview, telling her that the pre-teen hasn't always been convinced that her parents are cool.
"Blue, she's been fronting on me a little bit... but I catch her in the corner. You know now she asks me if I think this is cool, like my opinion on the sneakers she's wearing. She's come back. There was a time where she was like 'Dad!' I was like 'I'm cool! I don't know what you're saying. At your house, your parents are cool!"
Along with Blue, Beyoncé and Jay-Z are also parents to six-year-old twins, Rumi and Sir.
As well as her parents, Blue's grandmother Tina Knowles, has also been one of her biggest cheerleaders during her stage debut. The 69-year-old opened up about the 11-year-old's rising fame and talents during a star-studded gala held in New York City on Monday October 23.
Tina was talking to Page Six at The Angel Ball, telling the publication, "Blue tells me all the time, 'Grandma, you should come up there…' And I'm like. 'When am I going to find time to practice?' Because, you know, us old folks got to practice a lot longer than them. She learned it in like a week."
Tina previously praised Blue while chatting to People back in July, where she also touched upon the fact that her young granddaughter was able to dance effortlessly on stage in heels.
"Well, this is a heels family. You're trained early to walk in heels," she told the outlet. "But yeah, she's having the time of her life, and I couldn't be more proud of her because she really worked hard."
She added: "She is 11 years old, and she had one week to prepare, and she's just getting better and better. So I'm the proud grandma, always." When asked whether her granddaughter's confidence had seen a boost since joining the tour, she joked: "Oh, to the sky, to the sky. Yes."
Read more HELLO! US stories here
Get the lowdown on the biggest, hottest celebrity news, features and profiles coming out of the U.S. Sign up to our HELLO! Hollywood newsletter and get them delivered straight to your inbox.