The Spanish top seed, who has never won the season-ending event, came into the tournament at London's O2 Arena under an injury cloud and was well short of his imperious best as he went down 6-2 6-4 on Monday (November 11).
In the earlier round-robin match in Group Andre Agassi, sixth seed Tsitsipas beat Daniil Medvedev 7-6 (7/5) 6-4, admitting their spiky relationship had made his job tougher.
Nadal is locked in a battle with Novak Djokovic to finish as the year-end number one but was not serving flat out in practice last week due to an abdominal strain that forced him to pull out of the Paris Masters at the semi-final stage.
The 33-year-old led Germany's Zverev 5-0 in head-to-head contests coming into the match but was uncharacteristically sloppy in the first set, conceding two breaks of serve.
Buoyed by his dominant start, Zverev, seeded seventh, broke in the first game of the second set to take an iron grip on the match.
Nadal dug deep, urging himself on but his 22-year-old opponent proved too strong. He did not concede a single break point in the entire match.
Zverev hit a total of 26 winners -- double his opponent's tally -- and Nadal managed just three forehand winners in the entire match.
"The physical issue was not an excuse at all," said the Spanish 19-time Grand Slam champion, who said he did not feel any pain from his abdominal injury.
"The only excuse is I was not good enough tonight."
"What really matters is I need to play much better in two days. That's the only thing," he added.
"We knew that it was going to be tough, because the period of time since the injury until is very short, but we are here trying."
Zverev, one of four players under the age of 24 at the event in London, was delighted to recapture his best form after a mixed season.
"This means so much, playing here again after winning my biggest title so far in my career here last year," he said.
"This means everything to me.
"Playing here, playing in front of you all, playing in the O2 is something that we don't have during the year, and this is so special."
Nadal faces a tough task now to qualify for the semi-finals from the group phase, with matches still to come against Tsitsipas and Medvedev.
The Spaniard has qualified for the year-end championships for 15 years in a row but has only made nine appearances due to injuries.
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