The comedian - who has battled heroin addiction in the past - told The Sun that he feels guilty for not reaching out to the singer when he first noticed she was in trouble.
"I got clean at the age of 27, the age Amy was when she died," he explained. "[Her] death was a paradoxical unsurprising shock. I felt like I could have done something to help - to give her the chance I had.
"When she died, it was this feeling of, 'Agh, I knew that was going to happen'. I had this flickering sense that I should have done something about that. I feel a bit guilty that there was nothing I did."
Brand, 37, told the paper that he once ran into Winehouse at a party and could tell there and then she was struggling.
"I loved Amy on the basis that I thought she was really, really brilliant," he said. "I recognised that this person has got it, she has got this thing. She is not happy, she is on edge.
"She drank this glass of champagne and threw it over her shoulder once. I said, 'What are you doing that for?' She said, 'I was doing it to impress you'. I said, 'Well... don't', then she started flicking lit cigarettes around the room.
"That's when I got the sense of the ticking clock and spoke to other people, [saying]: 'Hey, we need to do something.'"
Brand, who appeared before the Home Affairs select committee as part of a discussion about drug policy in April, hopes to raise awareness and change attitudes towards addiction with his new BBC Three documentary Russell Brand: From Addiction To Recovery. He has described the programme as a "sympathetic look at alcoholism and addiction".
"Drugs and alcoholism are much misunderstood in our country - by users, non-users and the government," he said. "[It is] a condition that the World Health Organisation regards as a disorder. We need to start regarding addiction in all its forms as a health issue as opposed to a criminal and judicial issue."
'Russell Brand: From Addiction to Recovery' will air on BBC Three on Thursday, August 16 at 9pm.