Palace lost in a penalty shootout on Tuesday night after skipper Marc Guehi had found a 95th minute equaliser to cancel out Maxence Lacroix own goal.
Glasner said: “Of course, when you lose a game, when you lose on penalties, you're always disappointed.
“On the other side, I'm delighted with the second-half performance today, especially after the first-half performance – that was really bad. Walter Benitez kept us in the game, but the second-half was much better, it was an all-even game.
“We had already two penalty shootouts this year, and we won both, and today Arsenal were the lucky team. To be honest, I've watched many penalty shootouts in my life, but I can't remember having seen so many well-taken penalties. It's always somebody who has to miss, and today it was one of our players, but nobody is to blame.
"I spoke to the players. For us, it's important to build on the second-half performance and also show that great character again. All of a sudden, in the second half, one-nil down from a set-play, it looked like deja vu from the league game.
“Then, coming back again, with everything that’s happened in the last weeks and months, is a huge credit to the players for their mindset – so we'll take many positives from today's performance.”