Serena Williams,left, and Bianca Andreescu pose for photos after Andreescu won the US Open. Photo: Charles Krupa/AP Photo

NEW YORK  The Duchess of Sussex was in Serena Williams's box to witness the coronation of the queen of grand slam tennis. Instead, she saw a changing of the guard.

The American member of Britain's royal family watched in disbelief along with 24,000 others in the world's largest tennis arena as Williams first piled up the errors, then staged an astonishing comeback, only to fall short yet again to get a record-equalling 24th grand slam title.

"I believe I could have played better. I believe I could have done more. I believe I could have just been more Serena today," Williams said.

"I honestly don't think Serena showed up. I have to kind of figure out how to get her to show up in Grand Slam finals."

Williams, 37, fought from 5-1 and match point down to 5-5 before eventually losing 6-3, 7-5 to 19-year-old Canadian Bianca Andreescu, who had gone out in qualifying in New York last year and was playing in only her fourth career grand slam main draw.

"I know you wanted Serena to win, I am so sorry," said Andreescu, who named her opponent "a legend of the sport" after defying the partisan crowd before finally getting a big cheer as she lifted the trophy.

Williams won her first major 20 years ago at Flushing Meadows and moved within one slam title of Margaret Court's record 24 when she won the Australian Open in 2017.

Already pregnant at the time, she took a break to give birth to daughter Olympia two years ago, and returned last year to resume the chase.

But she lost back-to-back Wimbledon finals to Angelique Kerber and Simona Halep, plus last year's New York decider against Naomi Osaka under controversial circumstances over her row with chair umpire Carlos Ramos, who docked her a point and a game.

Ramos and Williams were kept apart this time around, and the biggest task for Saturday's umpire, Alison Hughes, was to contain the crowd during the remarkable Williams fightback.

Williams and her coach, Patrick Mouratoglou, had firmly believed in the title this time around: the 37-year-old had been back in action long enough after the maternity break, and had overcome back problems that forced her to retire early in the Toronto final - against Andreescu.

She routed ex-champ Maria Sharapova 6-1, 6-1 in the first round, only dropped one set en route to her 33rd grand slam final against 17-year-old Catherine McNally before further routs of Wang Qiang (6-1, 6-0) and fifth-seeded Elina Svitolina (6-3, 6-1).

But on Saturday she piled up 33 unforced errors to Andreescu's 17, had a low first-serve rate of 44 per cent, and handed her opponent three games with double faults: the very first one, the first set, and her first service game of the second.

Williams gained huge respect for her fightback amid a collective frenzy, but it wasn't to be once again, as Andreescu showed remarkable composure to wrap up matters after all.

It was another opportunity missed for Williams who, aside from Andreescu, will also feel the heat from two-time grand slam winner Osaka (21), Svitolina (24), McNally and soon also 15-year-old Coco Gauff, who became a huge fan favourite during her run into the third round.

But Williams has faced several generations of players during her career, from Martina Hingis in the 1990s and Kim Clijsters to Sharapova and Kerber, who beat her twice in grand slam finals, the Australian Open in 2016 and Wimbledon in 2018.

She has still managed to reach big finals and will surely be a factor to be reckoned with next year.

"I'm not necessarily chasing a record. I'm just trying to win grand slams. It's definitely frustrating, you know. But for the most part I just am still here. I'm still doing what I can do," Williams said.