Quentin Tarantino is standing by his fictionalized depiction of Bruce Lee.

The Oscar-winning writer and director, 56, included the late martial arts legend in his latest film Once Upon a Time… in Hollywood. The movie, which is set in 1969 Los Angeles, depicts Lee (played by newcomer Mike Moh) as cocky, giving him a whole monologue about how he could beat anyone in a fight.

But after fans and Lee’s family members, including his daughter Shannon Lee, slammed the portrayal as “caricature-like,” Tarantino is backing up his writing.

“The way he was talking, I didn’t just make a lot of that up,” Tarantino said at a press conference for the movie in Russia. “I heard him say things like that, to that effect. If people are saying, ‘Well he never said he could beat up Muhammad Ali,’ well yeah, he did. Not only did he say that, but his wife, Linda Lee, said that in her first biography I ever read … She absolutely said it.”

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While speaking with The Wrap after the movie’s release, Shannon expressed disappointment in how her father was treated onscreen “in the way that white Hollywood did when he was alive.”

“He comes across as an arrogant a–hole who was full of hot air,” Shannon, 50, an actress and martial artist herself, explained to the outlet. “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.”

Lee’s daughter added in her interview that while she “can understand all the reasoning behind what is portrayed in the movie,” it covers “a period of time that clearly had a lot of racism and exclusion.”

“It was really uncomfortable to sit in the theater and listen to people laugh at my father,” she said. “Here, he’s the one with all the puffery and he’s the one challenging Brad Pitt. Which is not how he was.”

Tarantino has also come under fire for showing Lee apparently being upper-handed by Brad Pitt’s washed-up stunt double Cliff Booth. While some criticized that it’s disrespectful to Lee’s talent to insinuate he would lose in a martial arts fight to the fictionalized stuntman, Tarantino once again defended the choice.

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“Could Cliff beat up Bruce Lee? Brad would not be able to beat up Bruce Lee, but Cliff maybe could,” he said to Russian press. “If you ask me the question, ‘Who would win in a fight: Bruce Lee or Dracula?’ It’s the same question. It’s a fictional character. If I say Cliff can beat Bruce Lee up, he’s a fictional character so he could beat Bruce Lee up.”

As for Moh’s performance, the late star’s daughter praised the 35-year-old actor’s accurate voice and mannerisms but noted, “I think he was directed to be a caricature” — and pointed out that Moh’s hairstyle and sunglasses were based on the look Bruce donned during his Enter the Dragon era in the early ’70s, before his death in 1973 at age 32. (Enter the Dragon was released posthumously.)

As Shannon previously recounted to PEOPLE, she was only 4 years old when she lost her father.

She said she has vivid memories of him and still feels a close connection.

“When he focused his attention on you, it was like having the sun shine on you,” Shannon said. “That feeling has stayed with me my whole life.”

Once Upon a Time… in Hollywood is now playing.