The 48-year-old Pirates Of The Caribbean star also insisted at the movie's European premiere at Odeon Kensington that the late Hunter S Thompson would have been impressed with the actor's work on the novel.
"I believe that Hunter would be very proud, yeah. He would probably try to hurt us a little bit with a sarcastic remark or whatever, but he would have been proud," he said.
It is the second time that Depp - who also produced the film - has portrayed the late gonzo journalist, who was also his close friend until his death in 2005, following his performance in Fear And Loathing In Las Vegas.
"There's more responsibility but there's also more fun in doing this," he admitted.
"He is someone I cared about, and still care about, and the main thing I wanted was to make him proud."
His co-star Amber Heard - who showed off her figure in a clinging sequinned dress by Alessandra Rich teamed with Christian Louboutin heels - described Depp as "wonderful".
"It was a dream job. Johnny has an intimate connection with the material and is wonderful to work with. I noticed that everyone would smile when he walks on set," she said.
About their kissing scenes, she joked: "His lips are professional!"
Click through our Slideshow of Johnny Depp, Amber Heard and Bruce Robinson at The Rum Diary premiere in London...
The Rum Diary, directed by Bruce Robinson, opens in cinemas on Friday November 11.