Rogers-Downey was at home with the Boogie Nights star when he died.
The Hollywood icon – who was known for directing breakthrough anti-establishment classic films such as Putney Swope and Greaser's Palace – had been battling Parkinson's for more than five years.
Robert Sr stayed away from the spotlight as much as possible, but previously spoke about the difficulties of being in Hollywood when talking about his son's struggle with fame.
He said in 2001: "Life is too easy when you're a movie star. People will do anything you want and get you anything you want. Hollywood is a horrible place."
The Magnolia actor also previously confessed to being addicted to cocaine at the height of his career, and stopped after being confronted by his wife and his son.
He explained: "Ten years of cocaine around the clock. I didn't beat it until '81, until my late wife gave me an ultimatum. I officially quit in front of my son. He keeps reminding me about it. I tell him, 'If it made such an impression on you, then why can't you do the same thing?'"
Robert Sr's most recent film project was 2011's Tower Heist, while his final directorial role was the 2005 documentary Rittenhouse Square.
