Damon was criticised after clashing with black film producer Effie Brown on his Project Greenlight show over who should direct a film being discussed.
He said diversity should be reflected "in the casting of the movie, not the casting of the show".
Damon said the comments were "part of a much broader conversation".
"I believe deeply that there needs to be more diverse filmmakers making movies," he said.
"I love making movies. It's what I have chosen to do with my life and I want every young person watching to believe that filmmaking is a viable form of creative expression for them too.
"My comments were part of a much broader conversation about diversity in Hollywood and the fundamental nature of which did not make the show."
Project Greenlight, which is broadcast on HBO, focuses on filmmakers who provide scripts to a panel of judges with the winner getting the 'green light' to make their film with a budget of $3m.
The project under discussion had a sole black character who was a prostitute, prompting Brown - who produced the critically-acclaimed Dear White People - to suggest the director would have to be carefully selected to handle the character "sensitively".
Damon's response that diversity is "what you do in the casting of the movie" drew an exasperated "Wow, okay," from Brown.
The comments were highlighted on social media and led to the coining of the term "Damonsplaining".
One user defined the term as "over talking and/or shouting down a person of colour to explain something about their own race or culture".
"I am sorry that they offended some people," said Damon in his statement. "But, at the very least, I am happy that they started a conversation about diversity in Hollywood. That is an ongoing conversation that we all should be having."
Actor Matt Damon has said sorry to people offended by his comments about diversity but said he is glad to have started a debate on race.