"I need to say that I have made mistakes in my personal life for which I am sorry," the baseball star said in a statement to the Houston Chronicle.
"Like everyone, I have flaws. I have sometimes made choices which have not been right."
Clemens, 45, and McCready's relationship became public last week when the pitcher was accused of having affairs with several women, including McCready, who was reportedly 15 when the two met.
Although McCready, 32, admitted to the affair with Clemens, a married father of two at the time, and her mother described the relationship as off and on, Clemens denies any wrongdoing.
"I have been accused of having an improper relationship with a 15-year-old girl. Nothing could be further from the truth," he said. "This relationship has been twisted and distorted far beyond reality."
Clemens's lawyer, Rusty Hardin, confirmed the relationship last week but said it was not sexual or "inappropriate."