In the tell-all book, aptly titled Putting The Rabbit In The Hat (out now) the Scottish star refers to Depp as "overblown" and "overrated".
He especially criticised Depp's performances in Tim Burton's 1990 film Edward Scissorhands and the Pirates of the Caribbean franchise, which Cox called "very much the 'Johnny Depp as Jack Sparrow' show."
"Personable though I’m sure he is, [Johnny Depp] is so overblown, so overrated." Cox writes.
Watch: Brian Cox 'honoured' to be part of Succession series
“I mean, Edward Scissorhands. Let’s face it, if you come on with hands like that and pale, scarred-face make-up, you don’t have to do anything. And he didn’t. And subsequently, he’s done even less,” continued Cox (via USA Today).
“But people love him. They don’t love him so much these days of course," he added, referencing Depp’s recent scandals involving his divorce to ex-wife Amber Heard.
Next on Cox's hit list was his The Glimmer Man co-star Steven Seagal, which he called “as ludicrous in real life as he appears onscreen.”
“He radiates a studied serenity, as though he’s on a higher plane to the rest of us. And while he’s certainly on a different plane, no doubt about that, it’s probably not a higher one.”
And while Cox praised Spike Lee as "simply one of the best directors I've ever worked with” he didn’t have kind words for Edward Norton — with whom he worked on Lee’s 25th Hour — saying he’s "a nice lad but a bit of a pain in the arse because he fancies himself as a writer-director."
Quentin Tarantino also found himself in Cox’s path. On him, the actor had to say: "I find his work meretricious. It’s all surface. Plot mechanics in place of depth. Style where there should be substance.
“I walked out of Pulp Fiction," confessed Cox, who added that he did sit through the director’s latest movie, Once Upon a Time in Hollywood, saying: “it wasn't as bad as I'd feared, it still wasn't good enough to convert me.”
Still, Cox admitted that he would still take the chance to star in a Tarantino movie: "If the phone rang, I'd do it."
Watch: Brian Cox return as Logan Roy in season 3 of Succession