Richardson, who was married to actor Liam Neeson and was the mother of his two sons, died last Wednesday of head injuries sustained in a skiing accident at the age of 45. She was buried Sunday in upstate New York.
Swayze has been waging a high-profile battle against pancreatic cancer for more than a year.
"It is such a great loss to this community to lose an actress and person such as Natasha," Swayze said in a statement issued to People.com. "Gifts like her don't come along very often. It's a rare thing in this industry to have someone with so much talent, beauty and dedication and yet is imbued with such humility. I know for me and many other people, the world will be a different place without her. My heart goes out to Liam and his two boys but I'm sure that Natasha's light is shining down on them."