Carey Mulligan stars as angst-filled folk singer Jean Berkey in the musical drama - which is competing for the prestigious Palme d'Or prize at Cannes Film Festival - and to land the part, she filmed a furious tirade for her audition tape which left the producer and director frightened.
Speaking at a press conference in Cannes, Joel recalled: "We saw a lot of actresses for this part but Carey sent us a tape and it's very funny."
Ethan added: "Funny because she was angry and p***ed off. It was a really angry reading of a scene with an American accent, and we were a little scared of her."
Meanwhile, the British beauty - who also stars in 'The Great Gatsby', which opened Cannes last week - "loved" playing the cruel character because she's so different from her previous roles.
Carey said: "I also loved how unkind Jean could be, how brutal even. Most of the women I play are quite empathetic and Jean most certainly is not."
However, the actress - who stars alongside singer-and-actor Justin Timberlake and Oscar Isaac in 'Inside Llewyn Davis' - admitted she found it "nerve-wracking" to sing on camera, especially alongside her musically gifted co-stars.
She added: "Singing, for me, seems to be the most nerve-wracking thing to do.
"And when you're surrounded by actual musicians like Oscar, Justin and Stark [Sands], it's even worse. Here I was with all these accomplished musicians so it was very intimidating."