The 41-year-old singer opened up about his friend - who tragically died nine years ago - and explained he struggles when he hears her songs on the radio.
He told the 'Walking The Dog' podcast: "If her music comes on I can’t listen to it.
“It’s too sad to think of the times where I could’ve of reached out.”
Jamie also revealed how he recently discovered old text messages from Amy, and described them as "a monument" to their friendship.
He added: "I found all her texts on an old phone. I’m sure anyone has that, where dead people are on your phone and you can’t delete their conversations.
“It was her and I just couldn’t delete them because it was a monument to a brief and lovely friendship.”
Earlier this year, Jamie's song 'The Age of Anxiety' was named Best Song Musically and Lyrically at the Ivor Novello Awards.
And he revealed the track refers to texts he received from Amy, and he described it as a song he "really believed in".
He previously said: "I'd been going through my studio and found some old phones and I did find a bunch of texts.
"Amy and I were good friends and my first tour was with her. She was my support act, if you can believe it."
Jamie was "extremely honoured" by the recognition in September, and he opened up about the origins of the single.
He said: "Someone was talking about me not sharing enough of my personal life, and I was feeling as if I wanted to jump out of the window.
"This line came to me: 'I just want to live inside sometimes.' "
The lyrics and track as a whole then became a "free association [of] all the things that make [him] feel anxious".