The band, comprised of Dublin schoolmates, has sold more than 150 million albums over a 40-year career.
But speaking on the Awards Chatter podcast, the 61-year-old said that, aside from 2004 track Vertigo, he finds it hard to listen to their music.
He added that his voice sounds "very strained" on earlier recordings.
"I've been in a car when one of our songs has come on the radio, and I've been the colour of - as we say in Dublin - scarlet," he told The Hollywood Reporter's Scott Feinberg during an hour-long interview.
"I'm just embarrassed. I do think U2 pushes out the boat on embarrassment quite a lot.
"And maybe that's the place to be as an artist is right at the edge of your level of pain for embarrassment, your level of embarrassment."
He added: "And the lyrics as well. I feel that on Boy and other albums it was sketched out very unique and original material. But I don't think I filled in the details."
In defence of his band, U2 have had 10 UK number one albums and seven chart-topping singles, since arriving on to the scene in the early 1980s.
Their fifth album Joshua Tree - featuring anthems like With Or Without You and Where The Streets Have No Name - was recently named as the best album of that particular decade by Radio 2 listeners.
While Bono agrees that his band "sound amazing", he said he does not like the sound of his own voice at all, except on Vertigo, which featured on How to Dismantle an Atomic Bomb. "Most of the other ones make me cringe a little bit," he said.
And despite a career spanning four decades, the Irish singer believes his voiced sounded weak early on and that he "only became a singer recently".
"I just found the voice very strained and kind of not macho and my Irish macho was kind of strained by that," he continued.
"A big discovery for me was listening to the Ramones and hearing the beautiful kind of sound of Joey Ramone and realising I didn't have to be that rock and roll singer.
"But I only became a singer recently."
'The one that we hated the least'
The singer appeared on the podcast alongside bandmate The Edge, who also revealed that the group was never particularly fond of its famous moniker.
U2, he explained, were originally supposed to be called The Hype, but ditched that plan as the name sounded unoriginal.
Their friend, the graphic designer Steve Averill then suggested some better ones. "Of the suggestions, it wasn't that it [U2] jumped out to us as the name we were really looking for, but it was the one that we hated the least," said the guitarist.
He said it sounded "fresh" at least at the time, and it was not "obvious from the name what this band would sound like or be about". "It was the one we chose and we didn't really love it at first."
"I still don't," offered Bono. "I really don't.
"But I was late into some kind of dyslexia, I didn't realise that The Beatles was a bad pun either." (The correct spelling of the insect is beetle.)
The band, he said, thought their name would conjure up "futuristic" images of "the spy plane" and "the U-boat".
"But then as it turned out to imply this kind of acquiescence, no, I don't like that name."
Bono and The Edge were appearing on the film awards season podcast to promote Sing 2, the Matthew McConaughey and Reese Witherspoon-starring animated film.
The singer voices a character in the film, while he and The Edge also co-wrote the song You Saved My Life from its soundtrack.