Williams exploded at umpire Carlos Ramos after being given a code violation for coaching.
Williams then demanded an apology from Ramos but later called him a “theif” after she was deducted a point for another code violation after a racket smash.
That saw Williams lose the game and fall 5-3 in the second set.
Osaka then served out the match to win her first Grand Slam.
Mouratoglou admitted Pam Shriver on ESPN: “I was coaching but I don’t think she looked at me.
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“Her coach [Sascha Bajin] was coaching the whole time, too. Everyone is doing it 100% of the time.
“It is not a big deal breaking a racquet. She will struggle to get back from this.”
Mouratoglou then said on Twitter: “The star of the show has been once again the chair umpire.
“Second time in this US Open and third time for Serena in a US Open Final.
“Should they be allowed have an influence on the result of a match?? When do we decide that this should never happen again?”
In her press conference, Williams hit back at Mouratoglou over his comments and said they will hold talks about the incident.
He said: “I literally just heard this. What’s he talking about? We don’t have signals.
“I’m trying to figure out why he would say that. I want to clarify for myself what he said. I wasn’t being coached.”