Perry was found dead at his home in Los Angeles on 28 October. He was 54.
Cox, 59, and Perry were cast as Monica and Chandler on the hit NBC sitcom, with the characters turning from friends to lovers over the 10-season run.
“I am so grateful for every moment I had with you Matty and I miss you every day,” Cox wrote on Instagram alongside a scene from the 1998 episode, “The One with Ross's Wedding”.
“When you work with someone as closely as I did with Matthew, there are thousands of moments I wish I could share. For now here’s one of my favourites.
“To give a little backstory, Chandler and Monica were supposed to have a one-night fling in London. But because of the audience’s reaction, it became the beginning of their love story.
“In this scene, before we started rolling, he whispered a funny line for me to say.
“He often did things like that. He was funny and he was kind,” she wrote.
Cox’s tribute comes hours after LeBlanc, 56, shared a tribute of his own.
LeBlanc played Chandler’s best friend Joey on Friends. The actor shared a series of stills from the show on Instagram alongside the caption: “It is with a heavy heart I say goodbye. The times we had together are honestly among the favourite times of my life.
“It was an honour to share the stage with you and to call you my friend. I will always smile when I think of you and I’ll never forget you. Never.
“Spread your wings and fly brother you’re finally free. Much love. And I guess you’re keeping the 20 bucks you owe me.”
LeBlanc was the first of the core Friends cast to pay tribute individually to Perry on social media.
In the emotional aftermath of his death, the lead stars released a joint statement asking for time to “process this unfathomable loss”.
They wrote: “We are all so utterly devastated by the loss of Matthew. We were more than just cast mates. We are a family. There is so much to say, but right now we’re going to take a moment to grieve and process this unfathomable loss.”
“In time we will say more, as and when we are able. For now, our thoughts and our love are with Matty’s family, his friends, and everyone who loved him around the world.”
Perry’s 3 November funeral service at Forest Lawn Memorial Park in the Hollywood Hills was attended by all of the core Friends cast members, including Jennifer Aniston, Lisa Kudrow, David Schwimmer, Cox, and LeBlanc.
Earlier this week, Perry’s death certificate was released by the Los Angeles Police Department.
According to the paperwork, his cause of death remains “deferred” pending further investigation, after initial toxicology tests revealed there was “no meth or fentanyl” in Perry’s system at the time of his death.