The 34-year-old Anderson still hopes to win a Grand Slam having lost finals to Rafael Nadal at the U.S. Open in 2017 and to Novak Djokovic at Wimbledon in 2018.
The two-time Grand Slam finalist wrote on Twitter on Friday that he had surgery Wednesday on a torn meniscus.
Kevin Anderson lost to Jason Jung 7-6, 6-4 on his return to the New York Open.
Serbia's Novak Djokovic defeated Kevin Anderson 7-6 (5), 7-6 (6) while Rafael Nadal got the better of beating Nikoloz Basilashvili 6-3, 7-5 for Spain.
The day's winners were Federer, Shapovalov, Barty, Pliskova and the rain.
World No.39 American beat the Indian qualifier in a match that lasted an hour and 52 minutes.
The 14-time Grand Slam champion played at a high level in all parts of the game in the semi-finals at London's O2 Arena on Saturday.
Zverev denied Roger Federer a shot at a 100th career title by beating the Swiss great 7-5, 7-6 (5) at the ATP Finals on Saturday.
Zverev is the youngest player at 21 to reach the semifinals since 2009 and the first from Germany since 2003.
Despite the resounding defeat, Nishikori's opening-match victory over Federer means he can still reach the semifinals for the third time.
On the back of his fifth ATP title, Anderson rose to World No. 6 joining Rafael Nadal, Novak Djokovic, Juan Martin del Potro, Roger Federer and Alexander Zverev in qualifying for the elite event.
They participated in the two longest semifinals in the history of a grass-court tournament that dates to 1877.
They had played on and on, through 6 1/2 hours of ho-hum hold after ho-hum hold, during the second-longest match in the history of a tournament that began in 1877.
The 29-year-old Argentine star beat three straight players ranked ahead of him in the hard-court event, topping No. 6 Dominic Thiem in the quarterfinals, No. 5 Alexander Zverev in the semifinals and eighth-ranked Anderson in finals.
Top seed Cilic from Croatia outplayed eighth seed Frenchman Pierre-Hugues Herbert 6-3 6-2 in 64 minutes while Anderson survived a mighty scare from a dogged Mikhail Kukushkin before edging him 6-7(3) 6-4 6-2.
The tournament ended without many of the stars who had been expected to take part in the six-player event.
The tournament has moved to Pune after being hosted in Chennai for 21 years
Rafael Nadal on Sunday beat South African Kevin Anderson 6-3, 6-3, 6-4 in the US Open final to win his 16th Grand Slam title
Nadal seeks his third US Open title after 2010 and 2013 and his 16th career Grand Slam title when he takes on Kevin Anderson.
The title was Zverev's first of his career on an outdoor hard court and gives him momentum heading into the U.S. Open, which starts Aug. 28.
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