The pair dated for seven years from 1984 to 1991.
Parker said that at 22, she often felt like Downey Jr.'s parent, telling the outlet that she tried to create stability around him in what was becoming a chaotic environment.
"People around him would be dismissive of me, but I had given him stability and tried to create a steady heartbeat that allowed him to show up on time," Parker said. "That made me angry and embarrassed me."
Downey, through a rep, told the magazine that he had "great respect" for Parker.
The pair met in 1984 after filming the thriller, Firstborn, and dated until 1991 as they both worked to establish themselves in Hollywood. Downey Jr. too acknowledged that his issues with substance abuse led to their downfall, telling Parade in 2008, "I liked to drink, and I had a drug problem, and that didn't jibe with Sarah Jessica, because it is the furthest thing from what she is," Downey Jr. said at the time.
He continued, "She provided me a home and understanding. She tried to help me. She was so miffed when I didn't get my act together… I was in love with Sarah Jessica, and love clearly was not enough."
He also admitted that he was "out of his mind," telling Howard Stern in a 2015 interview that he "did the best he could."
"We were in a very conservative relationship concerning the fact that she was normal and I was out of my mind," he said during an appearance on The Howard Stern Show. "I did the best I could."
While he was dating Parker, Downey Jr. starred in the war film 1969 with Kiefer Sutherland, which resulted in the trio "kind of" living together for three years.
"I would say, for Kiefer and I, [we] were almost always in a long-term, committed relationship and he is, and remains, a very disciplined guy despite whatever habits either of us had," Downey Jr. joked. "When we did the movie, I remember he'd be like, 'Robert, it's 6:15, it's time to go to work.'"
"He was probably staying with us for a while, and then I was having some trouble with Sarah Jessica, and he was looking after her," he continued. "It was all rather incestuous back then."
As for their current love lives, Parker moved on with husband Matthew Broderick, with whom she shares son James, 20, and twin daughters Tabitha and Marion, 13, with the pair celebrating their 26th wedding anniversary in May. Downey Jr., meanwhile, has been married to his wife, Susan, since 2005, welcoming a son, Exton, in 2013 and a daughter, Avri, in 2014. Downey Jr. is also dad to son Indio, 29, from his previous relationship with Deborah Falconer.