The 'Back to Black' singer was close friends with the former Libertines rocker, and before her untimely death from accidental alcohol poisoning last year, she had hoped to record some cover versions with her.
He said: ''We always planned to do some Billie Holiday songs together - 'Good Morning Heartache' and 'These Foolish Things'. Whenever we'd get together with guitars, we'd go through them.''
Pete, 33, also said he is ''resentful'' of Amy's death, and the fact he never got to say goodbye at her funeral.
He added: ''No one got the chance to say goodbye. It was such a shock. There are so many things I'm resentful of [about the situation], but I almost feel that it's not my business. I wouldn't want to offend anyone.
''A few times there have been tragic deaths of my friends, and their families have made me feel less than welcome in celebrating their memory. Like I was held responsible for these deaths.''
As with his Formula One documentary Senna, filmmaker Asaf Kapadia cleverly uses archival footage to...