Alcaraz eyeing triumphant Davis Cup farewell for Nadal after ATP Finals exit
World number three Alcaraz fell 7-6 (7/5), 6-4 to Zverev in Turin and has been eliminated as there is no combination of results between Andrey Rublev and Casper Ruud later in the day which can save him.
Rublev, who has lost his last six Finals matches, can still progress with a straight sets win over Ruud despite having lost his first two matches.
Alcaraz won Wimbledon and the French Open this season but struggled for form in Turin and will end his year alongside tennis icon and fellow Spaniard Nadal in Malaga next week.
Earlier in November, Davis Cup tournament director Feliciano Lopez said that a special ceremony would be organised for the 22-time Grand Slam winner, who will bow out on home soil.
"Probably one of the most special tournaments that I'm going to play. Last tournament of Rafa, I'll be able to be next to him in the last moments on a tennis court for him," said Alcaraz.
"I think it's most important for Rafa, for his last tournament. I really want him to retire with a title. It's going to be really, really emotional and a really special tournament for me."
Alcaraz leaves Turin having never performed to his full potential and at one point looking like he might even have to withdraw.
He played his final two matches in the John Newcombe Group wearing brink pink nasal tape after having problems breathing during a training session on Tuesday.
"It has been a difficult week, I guess, for me struggling with some physical problems, but at the same time it has been a really beautiful tournament," added Alcaraz.
"Today I faced one of the best players in the world, without a doubt, playing really solid and great tennis."
Zverev's Grand Slam goal
Zverev ensured he would advance when he took the first set after more than an hour of battle in northern Italy, before then sweeping through the second to complete a perfect group campaign.
German Zverev will face Taylor Fritz in the next round after gaining some form of revenge for defeat to Alcaraz in this year's French Open final.
The 27-year-old has a bittersweet relationship with Roland Garros as in the 2022 semi-finals he suffered an awful ankle injury and was forced to quit, allowing Nadal to reach the final and win his last Grand Slam.
Zverev has fought back from that injury to rise to number two in the world rankings and win two Master 1000 events this season, in Rome and Paris.
Those results that have given him confidence that he can win his first Grand Slam next year, with the Parisian clay his big target.
"Roland Garros is always marked in my calendar since the injury. I've been saying that the last few years," said Zverev.
"But for me, it's no secret, I'm searching for that Grand Slam title. I'm searching for world No. 1. I'm searching for the Grand Slams. If it's not Roland Garros, but it's Australia, I'll sign the paper right now, to be honest.
"Of course, it would be special if it's Paris. If it's anywhere else, I would be just as happy."
Zverev's qualification means that three of the four semi-final spots at the ATP Finals have been filled, with world number one Jannik Sinner and Fritz through from the Ilie Nastase Group.