The former Yazoo star has struggled with severe anxiety issues for years, resulting in her spending most of her time hiding from the outside world.
Now she has revealed she felt compelled to cut herself off after making a blunder during a chat with Costello after one of his gigs.
Speaking to Kirsty Young on the U.K.'s BBC Radio 4, she said, "I'd gone to see him (Costello) play in Southend (England) and he'd been brilliant. He'd sung this two-hour set and he was formidable. I absolutely loved it, and there was a party back at (U.K. band) Dr. Feelgood's house that he went to, and I'd been invited too, and there he was and he was lovely.
"He was charming and I wanted to say to him 'you were wonderful' and had all these wonderful descriptions of him. What came out of my mouth was, 'You dragged that out a bit, didn't you?' Once I did that, I just felt, I don't trust myself in polite society."
During the interview, which aired in the U.K. on Sunday (18May14), Moyet also revealed she smashed her gold records with a hammer and asked a shop assistant to delete all her songs from her computer when she took it in for repairs.
She added, "A year ago I took my computer to be mended and just told them to wipe everything without saving anything. That's my whole life - everything, my contacts, everything, my diary, everything gone, my songs, my demos, the lot - because I was really excited about having an empty inbox."