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."
Manchester United head coach Michael Carrick has urged everyone at the club, including the players and himself, to improve ahead of Sunday's Premier League clash against Bournemouth.
Joao Pedro has revealed how an early conversation with Cole Palmer helped build a friendship that has become central to Chelsea's attacking success.
Erling Haaland will be available for Manchester City's Premier League trip to Aston Villa on Saturday after recovering from the knock that ruled him out of their 5-1 Champions League victory over AEK Athens.
Bournemouth continued their perfect start to the Europa League league phase with a 3-0 victory over AC Milan, while Crystal Palace drew 2-2 with Besiktas in Istanbul and Juventus were held by Rennes by the same scoreline on Thursday.
