The Eagles went into the match on a 19-match unbeaten run and looked to be extending their streak after taking a 37th minute lead through a Daniel Munoz strike.
However, Everton managed to score twice in the last 14 minutes following many missed chances by the visitors, condemning them to their first loss since the 5-0 hammering against Newcastle United in April.
"We are very disappointed today," said Glasner to Sky Sports.
"About the result definitely, because I think 60-70 minutes we played so well. So really top, top performance. But it hurts really massively today. I think the last defeat was in April.
“But maybe we need this disappointment, this pain, to feel this pain to make the next step forward. So, from the last defeat we had a great learning (experience), and we will do now the same,” added the Austrian.
Palace head into the international break in sixth place on the Premier League table and having won their opening Europa League clash against Dynamo Kyiv in Poland.
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.
Manchester City are facing several late fitness tests as they prepare to visit Aston Villa on Sunday, with key midfielder Rodri among those in doubt.
