That accusation enraged Williams, who smashed her racket after being broken in the second set and was given a point penalty.
But Osaka - who displayed not only a stellar game but remarkable poise throughout - held serve to seal a historic win for her country.
According to the code of conduct, the first violation results in a warning, the second violation hands the player a point penalty, the third violation results in a game penalty and the fourth could force the player to forfeit the match. We don't have any code and I know you don't know that, and I understand why you may have thought that was coaching, but I'm telling you it's not.
"Osaka told ABC News Saturday evening that when Serena Williams hugged her at the end of the controversial match, it "really brought out the emotions" because when I was little and I was watching her play, I always wanted the opportunity to play her". You are the liar.You owe me an apology. You will never be on a court of mine as long as you live. How dare you insinuate that I was cheating... Say it you're sorry.
Williams took it up with tournament referee Brian Earley and called the penalties unfair: "This has happened to me too many times".
"I don't want to be rude, I don't want to do questions".
"We should not let her record, as glowing as it is, overshadow the fact that on this day, in this match Williams was wrong", Ings wrote in The Sydney Morning Herald. We're gonna get through this, and let's be positive. I don't think he knew if Serena saw the coaching or not.More news: What’s new in Tor Browser 8
"You shouldn't talk to anybody in this way whether they're an umpire or person on the street".
Last month, Williams black catsuit caused a stir at the French Open with the President of the tennis tournament asking Serena to "respect the game and the place" and banning the suit altogether.
"I'm honest, I was coaching", Mouratoglou ceded.
However, he said that all coaches coach from the' box, including Osaka's coach Sascha Bajin, and that he believes a change in the rules was needed. Everyone is doing it 100% of the time. "It's not a big deal to break a racquet", Mouratoglou said. "She will struggle to get back from this". For me, it blows my mind. "I have a daughter and I have not cheated in my life". I want to clarify myself what he's talking about.
The crowd booed in support of Williams.
Afterwards, the American said it was "sexist" to have been penalised a game. The multiple grand slam victor Victoria Azarenka said: "If it was a men's match, this wouldn't happen like this". And they're going to be allowed to do that because of today.
"When I step onto the court, I feel like a different person, right?" For tonight, it is time to celebrate these two fantastic players, both of whom have great integrity.
USTA chairwoman Katrina Adams released a statement Saturday night saying Williams actually showed "a great deal of class and sportsmanship" during the ceremony.