Palace fell to a defeat to the non-league side, ranked 117 places below in the football pyramid, after two goals either side of the interval with Paul Dawson and Isaac Buckley-Ricketts on target.
Yéremy Pino set up a grandstand finish with a late free-kick but it was not to be for the holders.
Glasner told Palace TV: "It's embarrassing. I've no explanation for what I've seen today. No excuse. It's really crazy, after experiencing the win in the FA Cup [last season] and now losing here.
"But congratulations to Macclesfield.
"I'm sorry we couldn't give them anything back today. At the end [full-time], the pitch was full of fans and people. Everybody just went into the dressing room.
"Everybody is disappointed. Players are frustrated. We didn't show up. We're sorry for that. I hope you can understand it.
"You, the fans and we all, are really disappointed.
"We will make a few changes and we will start again next week. Thanks for your support."