Strawberry said he was hoping to get help for his long-time friend.
Gooden, however, issued a statement to USA Today that read, "I don't do cocaine and have not in years."
He also went on Joe Piscopo's radio show on WNYM-AM and said, "Everything's good. I am healthy. I don't have a drug problem. I mean, I am an addict ... that don't mean I'm an active addict."
Gooden later told the New York Post, "He's trying to take the heat off himself, people who (are) in glass houses do not throw stones. He's cheating on his wife, he's having an affair with people. ...
"Darryl has a drug rehab in his name, he is supposed to be a pastor. I call him Lucifer. ... (Going public) was a weak shot, and he did it to make himself look better, because he is running a drug rehab."
Strawberry responded on ESPN Radio, "He's not Doctor K. He's an addict. ... He needs someone to help him, and I just felt like I needed to do this, regardless of what anyone thinks or says. As long as I know I did what I could to save his life."
Gooden's son, Dwight Gooden Jr., issued a statement that said his father's recent behavior -- including a no-show for a scheduled appearance with Strawberry at an event last week -- was caused by sadness over the recent death of Gooden Sr.'s mother and a busy work schedule.
"His problems have been well documented and publicized through the years," Gooden Jr. wrote. "At this time our only concern is his health and that he takes care of himself."
Gooden Sr., 51, played the first 11 seasons of his career with the Mets and was a four-time All-Star and won three World Series titles. He had a career 194-112 record with a 3.51 ERA and 2,293 strikeouts over 430 games.