Actor and martial arts expert Lee, who died in 1973 aged 32, rose to fame in the early '70s after the success of his Hong Kong-produced martial arts films films which included "The Big Boss" and "Fists of Fury", after struggling with stereotypical roles in Hollywood.
Shannon accused the director, who cast actor Mike Moh to play her father, of representing him "as an arrogant a**hole" in his film which is set in '60s Hollywood.
"(Bruce Lee) comes across as an arrogant a**hole who was full of hot air, and not someone who had to fight triple as hard as any of those people did to accomplish what was naturally given to so many others," she told the movie website The Wrap. "It was really uncomfortable to sit in the theatre and listen to people laugh at my father."
In the film Moh's Lee challenges stunt performer Cliff Booth, played by Brad Pitt, to a fight, in an encounter in which Booth gets the better of him, slamming him into a car door. According to Lee, her father would never challenge someone who was not versed in martial arts to a fight.
"(But) here, he's the one with all the puffery and he's the one challenging Brad Pitt. Which is not how he was," the late star's daughter insisted.
"I understand that the two (lead) characters are antiheroes, and this is sort of like a rage fantasy of what would happen ... and they're portraying a period that clearly had a lot of racism and exclusion," she said. "I understand they want to make the Brad Pitt character this super-bada** who could beat up Bruce Lee. But they didn't need to treat him in the way that white Hollywood did when he was alive."
Lee, who is president of the Bruce Lee Foundation and CEO of Bruce Lee Entertainment added, "What I'm interested in is raising the consciousness of who Bruce Lee was as a human being and how he lived his life. All of that was flushed down the toilet in this portrayal, and made my father into this arrogant punching bag."
Tarantino has not yet responded to a request for comment.