1222 GMT July 14, 2020
Ecclestone, 89, told CNN that "in lots of cases, black people are more racist than what white people are," BBC Sport reported.
Six-time world champion Hamilton, 35, said Ecclestone's remarks were "sad and disappointing."
He added they demonstrated "how far we as a society need to go before real equality can happen."
Hamilton, writing on Instagram, said, "Bernie is out of the sport and a different generation but this is exactly what is wrong.
"It makes complete sense to me now that nothing was said or done to make our sport more diverse or to address the racial abuse I received throughout my career.
"If someone who has run the sport for decades has such a lack of understanding of the deep-rooted issues we as black people deal with every day, how can we expect all the people who work under him to understand? It starts at the top.
"Now the time has come for change. I will not stop pushing to create an inclusive future for our sport with equal opportunity for all. To create a world that provides equal opportunity for minorities."
Hamilton's post came after F1 rejected Ecclestone's remarks and emphasized that he has "no role" in the sport.
F1 said in a statement that it "completely disagreed" with Ecclestone and that his comments "have no place in F1 or society."
F1 has launched an equality and diversity taskforce to increase opportunity for minority groups.