"I will continue to cherish your silliness, your perseverance, and your lovely heart," she said
Perry, 54, was found dead at his home in Los Angeles on Saturday.
"Two days ago, I woke up to the shocking news that Matthew Perry is no longer with us. It’s taken me a couple of days to process this profound sadness," Hayek Pinault, 57, wrote on Instagram Monday, sharing throwback photos of herself with Perry.
"There is a special bond that happens when you share dreams with someone, and together you work towards them," she continued. "I was very moved last year when Matthew shared on his Instagram stories how much he loved Fools Rush In, and how he thought that that film we did together was probably his best movie."
The actress said she stayed in touch with Perry in the time since making Fools Rush In.
"Throughout the years, he and I found ourselves reminiscing about that meaningful time in our lives with a deep sense of nostalgia and gratitude," wrote Hayek Pinault.
"My friend, you are gone much too soon, but I will continue to cherish your silliness, your perseverance, and your lovely heart. Farewell, sweet Matthew, we will never forget you."
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On Sunday, Perry's family said in a statement to PEOPLE that they are "heartbroken" by his "tragic" death.
"We are heartbroken by the tragic loss of our beloved son and brother. Matthew brought so much joy to the world, both as an actor and a friend," they said. "You all meant so much to him and we appreciate the tremendous outpouring of love."
The Los Angeles County Medical Examiner's Office confirmed to PEOPLE on Sunday that an autopsy was completed, with the results pending a toxicology report. The LAPD Robbery-Homicide Division is handling Perry's ongoing death investigation, and "foul play is not suspected at this time."
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