In the statement, she also announced that she's pregnant with her second child with her longtime partner, French actor Guillaume Canet.
Pitt, 52, and Cotillard, 40, both star in the upcoming film "Allied," which has the two in a romantic relationship. The juxtaposition of the film's promotion and Jolie Pitt filing for divorce from her husband sparked rumors online that the two co-stars were involved.
The French actress began her post by stating that it would be her only public reaction to the "whirlwind news" that she was "swept up into."
"Firstly, many years ago, I met the man of my life, father of our son and of the baby we are expecting. He is my love, my best friend, the only one that I need," she wrote.
"Secondly to those who have indicated that I am devastated, I am very well thank you. This crafted conversation isn't distressing," the Oscar winner continued. "And to all the media and the haters who are quick to pass judgment, I sincerely wish you a swift recovery."
She closed with a line of "respect."
"Finally, I do very much wish that Angelina and Brad, both whom I deeply respect, will find peace in this very tumultuous moment," Cotillard concluded.
Jolie filed for divorce on Monday, citing irreconcilable differences. She and Pitt had been together for over a decade, marrying in August 2014. They have six kids together.