Faithfull - who died in January at the age of 78 - made the admission in Broken English, a documentary which premiered on Saturday at the Venice Film Festival.
"The night before I did this (controversial TV) interview, Mick (Jagger) and I had taken LSD, and maybe that affected me," she said.
"But I think that some of my opinions and all that caused a lot of trouble - that I talked too much, too openly, and eventually what happened was that they came down on us."
The documentary also revisits the aftermath of the 1967 police raid on Jagger's Rolling Stones bandmate's Keith Richards' Sussex home, where Faithfull was famously found nude under a fur rug.
"It never occurred to me that the powers that be would ever do something like that, walk into Keith's house and arrest us," she said.
"I think Mick worried. He was quite straight … I really was like (a rock 'n' roll rebel.)
"I was very anarchic."
The film directed by Jane Pollard and Iain Forsyth, draws on archival material and new interviews.
Oscar-winning actress Tilda Swinton narrates sections of the project, while actor George MacKay interviews Faithfull in her final years.
Faithfull also spoke about her encounters with famous men, including Bob Dylan. Recalling a moment shown in DA Pennebaker's 1967 documentary Don't Look Back, she said: "A lot of tension. He was coming on to me. There was Joan (Baez.) I worshipped her.
"Bob said to me, 'I've been writing poem about you'.
"That's what he was typing. Well, it was probably completely made up.
"If I had a dollar for every cute man who's told me, 'This song, this poem is about you, darling, I'd be rich'."
Asked who some of those other men were, she replied: "I can't remember", before smiling.
The film also shows Faithfull discussing her songwriting partnership with Jagger and Keith Richards.
She explained Sister Morphine, the 1969 single later released by the Rolling Stones, began with Jagger playing a melody at home.
"It started as a lovely tune that Mick was annoyingly playing around the house all the time, so I decided to write lyrics for it," she said.
Broken English features live performances of Faithfull's songs by Beth Orton, Suki Waterhouse and Courtney Love, as well as contributions from Thurston Moore and members of Portishead and My Bloody Valentine.
It concludes with Faithfull's final filmed performance, singing her 2018 track Misunderstanding alongside Nick Cave.
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