Depp recently admitted he wasn't the friendliest person on set back then while accepting the Maltin Modern Master Award during the 31st annual Santa Barbara International Film Festival.
"I tortured him," the Oscar-nominated actor said Thursday, according to People magazine.
"It was a hard time for me, that film, for some reason. I don't know why," Depp, 52, recalled of filming the family drama.
"[DiCaprio] was always talking about these videos games, you know? I told you it was kind of a dark period," he added. "'No, I will not give you a drag of my cigarette while you hide from your mother again, Leo.'"
Still, Depp said he had great respect for DiCaprio, 41, as a young actor.
"I'd say the absolute truth is that I respect Leo a lot. He worked really hard on that film and spent a lot of time researching. He came to set and he was ready to work hard and all his ducks were in a row."