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."
Nottingham Forest are set to receive a double injury boost ahead of their Premier League showdown with champions Liverpool after the international break, with both Chris Wood and Callum Hudson-Odoi expected to return to action.
David Moyes has praised James Garner for his outstanding form this season, saying the Everton midfielder is edging closer to an England call-up.
Leeds United manager Daniel Farke has provided a detailed update on the club's injury situation as the Whites head into the international break aiming to reset after a frustrating run of results.
Arne Slot believes Liverpool's toughest spell of the season is now behind them, with a crucial run of winnable fixtures offering a chance to reignite their campaign after a heavy defeat to Manchester City.
