The television cameras caught Sabalenka letting out her frustrations once she had left the court.
Eurosport published a video showing the 25-year-old smashing a racket in the warm-up area before then calmly throwing it in the bin.
The video was out of the view of the public and there was no one else around.
Judy Murray criticised the decision to publish the footage and wrote on X: “This footage should never have been made public. A private moment in an empty training room after the disappointment of losing a Grand Slam final.”
Sabalenka had every right to be frustrated as she threw away a one set lead against Gauff.
She started the match well in the fierce atmosphere inside the Arthur Ashe Stadium as her every error was met with a booming cheer.
The new world number one was given a brilliant ovation by the crowd in her speech after the match was over.
She joked: “You guys could have supported [me] like this during the match.”
In her post-match press conference, Sabalenka added: “The crowd? I didn’t play against the crowd, I received many messages of support when I was here, but obviously in the final the crowd supported her and not me.
“She is 19 years old , she’s American and she’s playing a Grand Slam final, all of this is incredible and that’s why tonight we can say that she wrote history. I expected this atmosphere, I didn’t want to react to the public because I knew they would charge even more, but she felt comfortable with herself and it showed on the court.
“Sometimes I get too emotional, today on the pitch I thought too much and made so many absurd mistakes. In the second set I made a lot of it and I helped her not only to get back into the match but also to make her believe she could win.
“It was a challenge against myself. Overall it’s a huge achievement and I’m proud of myself. Now my goal is to finish the season in first position, reach the top and stay there.”