The Beatles legend met the "Rehab" star at the MTV Europe Awards in Liverpool in 2008, three years before the singer died from alcohol poisoning at the age of 27, and he admits he should have said more than a casual 'hello'.
"I knew she had a problem, and I ended up just saying hi, she said hi," McCartney tells GQ, recalling his brief chat with Amy backstage.
"Afterwards I thought I really should have just run after her (and said), 'Hey, Amy, listen, you're really good, I really hope you...', and say something that broke through the despair. And she'd remember and think, 'Oh yeah, I'm good, I've got a life to lead'.
"But you always have those little regrets."
The veteran rocker was extremely candid in his GQ interview, hitting headlines earlier this week with revelations that he once had a threesome with two hookers in Las Vegas and masturbated in front of bandmate John Lennon and a group of friends.
"He did very kindly offer to produce this album, and then I thought, 'No'. I kind of knew what direction I wanted to go in. And I knew that would be very different from where Kanye would go with it. I said, 'That's great, wow!' I'm just amazed that he said it. And then we never talked about it again. It was just a thought that was thrown away. I certainly thought about it and got very excited."