"Michael joins me in thanking you all for your overwhelming love, kind words and prayers since the passing of my father in law Kirk," she captioned the photo. "My whole family appreciated every word. Love to you all❤️"
Michael also posted a tribute online following his dad's death, writing in part, "Kirk's life was well-lived, and he leaves a legacy in film that will endure for generations to come, and a history as a renowned philanthropist who worked to aid the public and bring peace to the planet."
"I love you so much and I am proud to be your son," he added.
On Friday, Kirk was laid to rest at the Pierce Brothers Westwood Village Memorial Park and Mortuary in Los Angeles. Catherine and Michael were in attendance, as was Kirk's wife of 65 years, Anne Buydens, and his two other sons, Peter and Joel Douglas. Michael's son, Cameron Douglas, also attended the funeral.