Maybe someday in the distant future, Serena Williams will look back and be proud of herself for making it to the final at four of the first seven Grand Slam tournaments she played in after having a baby.

But not right now.

Last Saturday night, Williams, as fierce a competitor as tennis has seen, could only focus on the fact that she lost each of those title matches. The latest instance came earlier Saturday at the U.S. Open, when she was beaten 6-3, 7-5 by 19-year-old Bianca Andreescu of Canada.

With the victory, Andreescu won her first major championship and stopped Williams from claiming a record-tying 24th.

“I feel like, in 20 years, I definitely will be like, ‘Wow, that wasn’t so bad,’ ” the 37-year- old Williams said, her words halting, her voice scratchy. “It’s very hard right now in the moment to, like, take this and say, ‘It didn’t work out for you today.’ It’s really hard right now to take that moment in and to say, ‘You did OK,’ because I don’t believe I did.”

Williams has not won a title of any sort since the Australian Open in January 2017. That allowed her to break a tie with Steffi Graf for most Grand Slam titles in the Open era, which began in 1968, by collecting No. 23.

Only Margaret Court, with 24, has more in the history of tennis.

“Nobody has pressure like Serena. No one,” said Williams’ coach, Patrick Mouratoglou, who was cited for trying to send Williams signals in last year’s U.S. Open final, leading to a series of arguments between her and the chair umpire.

“She’s playing for history. She’s playing one match for his- tory. There is no bigger pressure than that,” Mouratoglou said. “That she’s a bit tight is normal.”

Williams gave birth in September 2017, and since returning to the tour last year, she has managed to play in two finals apiece at Wimbledon and the U.S. Open. Each time, she fell short of victory. And each time, Williams lamented not quite playing up to her own high standards.

The losses have come against Naomi Osaka, Angelique Kerber, Simona Halep and, now, Andreescu.

“All of it honestly, truly is super frustrating. I’m, like, so close, so close, so close, yet so far away,” Williams said. “I don’t know what to say. I guess I’ve got to keep going if I want to be a professional tennis player. And I’ve just got to just keep fighting through it.”

Williams started poorly against Andreescu, who was seeded No. 15 and playing in her first major final and her debut in the main draw at Flushing Meadows. Williams double-faulted twice in a row to drop the very first game.

She wound up with eight double-faults, three that came on break points, and made a total of 33 unforced errors, nearly twice Andreescu’s 17.

Trailing by a set and 5-1 in the second, Williams erased one match point and prolonged the match, eventually getting to 5-all. But she wouldn’t win another game.

“I believe I could have played better. I believe I could have done more. I believe I could have just been more Serena today,” said Williams, who turns 38 this month and was the oldest major finalist in the Open era. “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.”

Andreescu, the first player from Canada to win a major singles title, was happy and relieved at her victory.

“Being able to play on this stage against Serena, a true legend in this sport, is amazing,” Andreescu said. “Oh, man, it wasn’t easy at all.”

Rooting Williams on from the tennis star’s box was Meghan Markle, the Duchess of Sussex. Ms. Markle sat in Williams’ box at Arthur Ashe Stadium in New York and stood and cheered like thousands of other fans when Williams hit a booming overhand to win a point in the first set. The former actress-turned-royal, who starred in the cable show “Suits,” sat in front of fashion influencer Anna Wintour and behind Williams’ husband Alexis Ohanian. Ms. Wintour wore her usual dark shades and did not crack a smile when she was shown on the big screen as the song “Vogue” by Madonna blared through the stadium.

By comparison, Ms. Markle smiled and waved to a cheering crowd as she was billed on the screen as “HRH The Duchess of Sussex.”

The Duchess wore a belted denim long-sleeve dress and headlined the A-list starpower that attended the U.S. Open final: Spike Lee, Andy Cohen and Taraji P. Henson were among the big names in the stands.

Ms. Markle struck out as serving as a good luck charm for Williams. She was Briefcase Model No. 24 — the number of slams Williams was trying to reach — when she appeared on the TV show “Deal or No Deal.”

While her appearance at Flushing Meadows sparked a media blitz, the royal family is a constant presence at Wimbledon.