The result spoilt what was supposed to be a historic European occasion for the club.
It was Palace's first-ever home match in the main draw of a major European competition in their 101-year history, but Cypriot side Larnaca stunned Selhurst Park thanks to Riad Bajic's clinical 51st-minute strike.
The result ended Palace's 14-match unbeaten home run in all competitions and came just five days after their thrilling 3-3 Premier League draw with Bournemouth. Despite being eighth in the Premier League and FA Cup holders, Glasner said the defeat served as an important lesson.
"We will learn from it, the players will learn. It's disappointing and frustrating, but maybe the whole environment needed it to stay humble," Glasner told reporters.
"You are always told that if you play in the Premier League, you automatically win the Conference League. Stay humble. I don't know if any debutant has ever won this competition, I don't think so."
Palace dominated possession but lacked composure in front of goal. Jean-Philippe Mateta, fresh from his hat-trick at the weekend, squandered several key chances, including a golden opportunity created by substitute Eddie Nketiah midway through the second half.
Maxence Lacroix also went close, heading narrowly wide from a Will Hughes cross, while Nketiah failed to convert another inviting delivery late on.
Larnaca, who are fifth in the Cypriot First Division, defended resolutely and punished Palace's defensive lapse when Bajic capitalised on a mix-up to fire past Dean Henderson.
Glasner made attacking changes in search of an equaliser, but Palace's profligacy continued as they fell to their first home defeat since February. The loss left them with one win and one defeat from their opening two league-phase games.
Palace now turn their focus back to domestic action with a daunting trip to Premier League leaders Arsenal on Sunday, where Glasner will be demanding a reaction.
"It's about how we respond," he said. "We must remember what got us here, hard work, discipline, and humility."
Liverpool manager Arne Slot has backed Mohamed Salah to rediscover his scoring touch as the Egyptian forward looks to end his six-match goal drought ahead of Saturday evening's Premier League trip to Brentford.
Unai Emery admitted his frustration after Aston Villa fell to a shock 2-1 defeat against Dutch side Go Ahead Eagles in the UEFA Europa League on Thursday night in Deventer.
Sean Dyche made an immediate impact at Nottingham Forest as his side ended a 10-game winless run with a 2-0 triumph over Porto in the Europa League on Thursday night, the club's first European win since 1995.
Liverpool's dominant 5-1 Champions League victory over Eintracht Frankfurt was overshadowed by a major injury setback, as Jeremie Frimpong suffered a recurrence of his hamstring problem that will keep him out for several weeks.
