Alcaraz's 7-6 (7-5) 6-4 loss to Alexander Zverev meant the French Open and Wimbledon champion, who has been sick this week, was eliminated from the elite, eight-man tournament in Turin.
In Saturday's semi-finals, Zverev will meet Taylor Fritz and top-ranked Jannik Sinner will play Casper Ruud.
"My goal," Alcaraz said, "(is) to be at the end (of tournaments) all the time.
"Every tournament that I'm going to play at least reach the semi-final, final. So I have to work. ... In 2025, I hope to be a better player and (have) more consistency."
Ruud advanced by beating Andrey Rublev 6-4 5-7 6-2.
Zverev finished with a perfect three victories to win his round-robin group. Ruud had two wins, Alcaraz had one and Rublev had none.
Carlos Alcaraz now aims to give teammate Rafael Nadal the perfect send off in the Davis Cup Finals. (AP PHOTO)
Alcaraz turned on the style in the final game but lost a crucial point when he couldn't fully reach a Zverev passing attempt and ended up sprawled on the court.
"He turns into a different person. He really plays his best at the most important moments," Zverev said. "The last game was the most entertaining game of the match."
Sinner won the other group ahead of Fritz.
Alcaraz again wore a pink nose strip after struggling with breathing issues in his opening loss to Ruud.
Zverev leapfrogged Alcaraz to No.2 in the rankings this week and took a 6-5 edge in their career meetings.
It was a measure of revenge for Zverev, who was beaten by Alcaraz in five sets in the French Open final.
Zverev has bigger goals than reaching No.2 for next year.
"It's no secret, I'm searching for that grand slam title. I'm searching for world No.1," he said. "If it's not Roland Garros, but it's Australia, I'll sign the paper right now."
Alcaraz was already looking ahead to Malaga and next week's Davis Cup Finals, where he will play for Spain in Rafael Nadal's swansong.
"I really want him to retire with a title," Alcaraz said. "It's going to be really, really emotional and a really special tournament for me."
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