Williams, beaten in straight sets by Naomi Osaka, was docked a game for verbal abuse, having already had a point penalty for smashing her racquet and a code violation for coaching.

The American, 36, later said it was "sexist" to have been penalised a game.

"Serena was out of line, there's no question," said compatriot King.

King, one of the founders of the Women's Tennis Association (WTA), initially backed the 23-time Grand Slam champion, saying in the aftermath of Saturday's final: "When a woman is emotional, she's 'hysterical' and she's penalised for it. When a man does the same, he's 'outspoken' and there are no repercussions.

"Thank you, Serena Williams, for calling out this double standard. More voices are needed to do the same."

However, in an interview with CNN on Tuesday, King's stance softened.

"No-one was saying she was a good sport, if they are they're crazy," added the 74-year-old, who won 12 Grand Slam singles titles.

"The point is he [Ramos] aggravated the situation, instead of 'I'm not attacking your character' which is the most important thing he could have said."

Williams' claims of sexism were backed by the WTA, but the International Tennis Federation said Ramos acted "at all times with professionalism and integrity".

"I felt like he blew it," said King. "First of all as an umpire you're supposed to keep the flow of the match going and he did just the opposite.

"He needed to tell Serena he can't apologise, he did the right thing there, he's got to be the boss - but all he had to say to Serena is: 'I am not attacking your character.'

"Character is the essence of what was going on there, she was so upset about that. Those kids [Serena and her sister Venus] have been brought up to play by the rules.

"The character was the biggest issue here. This is a human being you're talking to. If he had said 'I'm not attacking your character' everything would have been different."

Umpire says he is 'fine'

The umpire at the centre of the controversy insists he is fine - and says it is not possible to umpire a tennis match "a la carte".

Ramos spoke very briefly about the US Open final to Tribuna Expresso in his native Portugal.

He is expected to be on duty as planned for this week's Davis Cup semi-final in Zadar, where Croatia are hosting the United States.

"It's a delicate situation," Ramos said. "But umpiring a la carte is something that does not exist. Don't worry about me, I'll be fine."