The pair met in 2008 to discuss the possibility of Winehouse writing a ballad for the 007 franchise.
Her song was meant to feature in Quantum of Solace, starring Daniel Craig.
Broccoli said that “Back to Black” singer was “very fragile emotionally” when they met.
“Well, that was a very, very distressing meeting. She was not at her best and my heart really went out to her,” Broccoli told Entertainment Weekly.
“She was very fragile emotionally, and you know, you understood how she could create such moving material, because she has a great depth of feeling and it was very, very tragic.”
Broccoli added: “What an incredible talent, what an incredible voice, what an incredible person she was. And it was very, very sad.”
The Quantum of Solace theme song – titled “Another Way to Die” – was instead recorded by Jack White and Alicia Keys.
Earlier this year, White said that they were asked to step in because Winehouse “wasn’t showing up to the sessions or wasn’t delivering the song that they were asking her to do”.
Winehouse died aged 27 on 23 July 2011.
Billie Eilish was behind the latest Bond theme song. The singer and her brother Finneas became the first American songwriters to win Best Original Song for their song “No Time To Die”, which featured in the Daniel Craig film last year.
The previous two Bond movies, Skyfall and Spectre, also won Best Original Song for their themes by Sam Smith and Adele, respectively.
James Bond alum Pierce Brosnan was not convinced by Craig’s final outing as Bond.
On Craig’s 15-year tenure as Bond, Brosnan said: “I saw the last one and I saw Skyfall. I love Skyfall. I’m not too sure about the last one.”