The Eagles were well on top in the first-half and fully deserving of the lead which Daniel Muñoz gave them shortly before the interval, as the Colombian rounded off a fine team move involving Marc Guéhi, Yeremy Pino and Ismaïla Sarr.
But despite continuing to create plentiful more chances after the restart, two late defensive errors saw the Toffees turn things around inside the final 15 minutes to inflict a painful first loss of the season on Palace.
Glasner told Palace TV: “It's disappointing and very painful because it's completely unnecessary. It's our fault, it's our responsibility. We played so well over 60 or 70 minutes with enough chances to decide the game.
“[Tiredness] would be a cheap excuse. We're never looking for excuses. We could have decided it in the first 60 minutes, an