In an interview with fashion magazine Harper's Bazaar published Tuesday, Williams revealed that she started seeing a therapist after being unable to "find peace" following her match against Osaka.
Chair umpire Carlos Ramos issued three code violations to Williams during the U.S. Open final, resulting in the loss of a game.
The first warning violation came after Ramos believed Williams was receiving coaching from her box. Williams lost the next point and smashed her racket in frustration, resulting in another violation and a point being awarded to Osaka. The third came after Williams called Ramos a "thief."
Williams, who advanced to the Wimbledon semifinals Tuesday by defeating Alison Riske in three sets, said she wrote an apology message to Osaka for her behavior.
"Days passed, and I still couldn't find peace. I started seeing a therapist. I was searching for answers, and although I felt like I was making progress, I still wasn't ready to pick up a racket," Williams said. "Finally I realized that there was only one way for me to move forward. It was time for me to apologize to the person who deserved it the most."
Williams said she was a fan of Osaka, adding that she was "truly sorry" in her message to the Japanese star.
Osaka responded to the apology, Williams said. Williams added that she began to cry when she read Osaka's response.
"When Naomi's response came through, tears rolled down my face," Williams said. "It was in this moment that I realized the real reason the U.S. Open was so hard for me to get over: It wasn't because of the backlash I faced but rather because of what had happened to the young woman who deserved so much more in her special moment."
Williams, 37, will play either Johanna Konta or Barbora Strycova in the semifinals at Wimbledon.