Serena Williams has been fined a total of $17,000 (approximately £13,000) for her offences during the US Open final.

The 23-time grand slam champion lost her cool after being given a warning for coaching from the stands early in the second set against Japan's Naomi Osaka.

She was penalised a point for a second offence, smashing her racket, and then a game after she verbally abused umpire Carlos Ramos, calling him a liar and a thief. That put Williams 5-3 down in the second set and she went on to lose 6-2, 6-4.

The verbal abuse offence was the most serious and, for that, Williams has been docked $10,000 (£7,700). The remainder of the fine is made up of $4,000 for coaching (£3,100) and $3,000 for racket abuse (£2,300).

She earned $1.85m (£1.43m) in prize money for reaching the final.

This was supposed to be the day when Williams finally equalled the all-time record of 24 grand slam singles titles won by Margaret Court and more than 23,000 fans packed into Arthur Ashe Stadium eager to be a part of her moment.

But instead the final descended into rancour as Williams and Ramos, a very experienced Portuguese official, took centre stage, overshadowing a remarkably composed performance from 20-year-old Osaka in her first grand slam final.

Williams was furious when she was given a coaching violation after Ramos spotted a hand gesture from her coach Patrick Mouratoglou, telling the umpire she would rather lose than cheat.

Mouratoglou later admitted to ESPN that he had been coaching, but Williams insisted she had not seen the signal and that they had never discussed such communication.

Mouratoglou, who has worked with Williams since 2012, alleged Osaka's coach Sascaha Bajin was also coaching, and it is an open secret that such conduct is commonplace.

On-court coaching is allowed on the WTA Tour, but Williams is one of the few players who never uses it.

After dropping serve in the fifth game of the second set and smashing her racket, Williams was given an automatic second violation, resulting in a point penalty, something of which she initially seemed unaware.

She continued her argument with Ramos at the next change of ends and accused him of being a thief for taking a point away from her. Ramos gave her a third violation, which resulted in a game penalty.

A tearful Williams argued her case with tournament referee Brian Earley and grand slam supervisor Donna Kelso, claiming a male player would not have been punished in such a situation, but a tournament statement later confirmed the umpire's decisions were final.

Asked in her press conference what she would have done differently in hindsight, Williams became increasingly emotional as she said: "I can't sit here and say I wouldn't say he's a thief, because I thought he took a game from me.

"But I've seen other men call other umpires several things. I'm here fighting for women's rights and for women's equality and for all kinds of stuff. For me to say 'thief' and for him to take a game, it made me feel like it was a sexist remark. He's never taken a game from a man because they said 'thief'. It blows my mind."

Osaka, meanwhile, attributed her composure during a wild first grand slam final partly to her sister's taste in bakery products.

The 20-year-old became Japan's first grand slam singles champion following Williams' meltdown.

Osaka did not waver serving either for the first set or the match and time and again drew the error from Williams, who was appearing in her 31st slam final, rather than the other way around.

Osaka revealed she was not quite coolness personified, though, saying: "I woke up and I was sweating. I was so nervous. My heart was racing the entire day. I think that wasn't good for my health.

"I couldn't eat anything, I felt like I was going to throw up. I was just so stressed and I kept calling my sister, my poor sister. She was telling me to think of it as just another match and then I would yell at her, 'Are you crazy? This is a grand slam final.'

"Since she's in Paris, she was showing me these random croissants and baguettes to try to take my mind off of it, and it kind of worked."

Osaka's sister Mari is also a tennis player and they were coached by their father after he decided to try to copy Richard Williams' remarkable success with his daughters.

Mari has not yet had the same rise as her younger sister and is currently playing lower-tier events after a series of injuries.

Osaka's father, Leonard Francois, gets so nervous he cannot watch his daughter in action, but she credits him for her big-match mentality.

She said: "Ever since I was little he's always been telling me these wise words but I've never really wanted to listen. I think that as I grew up I sort of appreciated what he was saying more. It's the most cliched things you could think of, always things that make you go 'Ugh'."

Osaka grew up idolising Williams – and insisted what happened on Saturday would not change that, even though the shine was certainly taken off her big moment.

With this victory and the manner of it, she has positioned herself as the next big hope to succeed Williams as the dominant force in women's tennis.

One thing that is certain is that Osaka's stock around the world, but particularly in Japan, will skyrocket.

She will head to Tokyo from New York ahead of the Pan Pacific Open, beginning on September 17, and it is likely to be some homecoming for the player born in Japan but raised in the United States.

Osaka's current clothing contract with adidas runs out at the end of the year and she is now perfectly positioned to secure a multi-million-dollar deal, along with many other endorsements.

Her agent Stuart Duguid said: "I don't think Naomi knows what's coming, but I have a fair idea."