Nash, who was 86, was killed alongside his 82-year-old wife Alicia when their taxi crashed in New Jersey on Sunday (May 24).
"Their lives ended together in the same way that they lived," Grazer told Variety.
"Theirs was a such a brilliant collaboration. Alicia was so powerful in enabling him to have his moments of triumph.
"His life was really hard. The beauty came from the power of their love to create those triumphs."
Grazer also recalled the time he 'auditioned' for the couple before production on the film began.
"I asked them, 'When the movie is finished and you're in the theater watching it, what is your fantasy of the experience?'"
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"Alicia responded by saying 'If the story is about love, we'll feel really comfortable'. And that idea was such a guiding force of our movie."
Speaking about attending the Oscars with the couple in 2002, Grazer said: "That night was the first time I saw them both smile."
A Beautiful Mind star Russell Crowe, who played John Nash in the movie, tweeted his sympathies to the Nash family, saying he's "stunned" by the news of the couple's passing.
Stunned...my heart goes out to John & Alicia & family.
An amazing partnership. Beautiful minds, beautiful hearts. https://t.co/XF4V9MBwU4
— Russell Crowe (@russellcrowe) May 24, 2015
A Beautiful Mind's director Ron Howard also paid tribute to the couple, writing: "It was an honour telling part of their story."
"John's remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, ground-breaking work in game theory," added Christopher Eisgruber, president of Princeton University.
"The story of his life with Alicia moved millions of readers and moviegoers who marveled at their courage in the face of daunting challenges."
Watch a trailer for A Beautiful Mind below:
