The Northern Ireland-born New Zealand actor, best known for playing Dr Alan Grant in the blockbuster franchise, died aged 78 in Sydney, Australia, on Monday.
His death came months after he announced he was cancer-free following treatment, three years after saying he had a "ferocious" and aggressive form of non-Hodgkin lymphoma.
Neill starred in Taika Waititi's 2016 comedy Hunt For the Wilderpeople alongside Rima Te Wiata, and she said the actor had a bout of pneumonia prior to his death.
In an interview with NZ Herald, she said: "It really sucks.
"I'm sure, as he said in the press once, he's not scared of death, but he would be annoyed.
"He would be like, 'Oh, for goodness sake! I got over my cancer, and now look, now I get pneumonia. What next?'
"But he's on his big journey now."
She also paid tribute to Neill, saying: "To be a really good actor, you've got to be a good listener. He had really good instincts and a really good spirit. He had a lot of empathy, and those qualities really helped him.
"He had compassion for his characters, even if they were awful. He knew how to understand things from their perspective."
Tributes have poured in for the actor, who was also known for portraying the corrupt senior police officer Major Chester Campbell in the first two seasons of Peaky Blinders opposite Cillian Murphy.
Former child star Joseph Mazzello, 42 - joined a host of Jurassic Park stars to share their grief at Neill's passing, saying his death was a "gut punch".
Mazzello said Neill was "the best of us", adding: "I can't say enough good about it and it's just still shocking, and I'm going to miss him."
Co-stars Laura Dern and Jeff Goldblum also paid tribute following his death.
Dern said: "Sam was my beloved lifetime friend… He showed me the depths of loyalty, protectiveness, and love, always with the driest of wit. He was a true and noble gentleman, wrapped up in my dream leading man. I will love you forever, Dr Alan Grant."
Goldblum said: "The next great adventure begins. Love, always and forever."
Jurassic Park director Spielberg said in a statement he "adored" making movies with Neill.
"We will always have our Jurassic family, and Sam will never be forgotten by us or his many millions of fans around the world," he said.
Neill reprised his role as Grant in 2001's Jurassic Park III and Jurassic World Dominion in 2022.
Bryce Dallas Howard - his co-star from the latter movie - described Neill as "funny, warm, wickedly self-deprecating, endlessly kind".
Chris Pratt - who played Owen Grady in the first three films of the Jurassic World franchise - said he was "devastated" to hear the news.
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