The Madejski Stadium club blew a four-goal lead to lose 7-5 after extra time in the fourth round in what was an incredible game.
McDermott was annoyed Arsenal were able to equalise at 4-4 in the sixth minute of added time at the end of the 90 when only an additional four minutes had been scheduled.
And he said: "If it's four minutes, you don't mind another 30 seconds but not another two minutes. I was waiting for him to blow his whistle but he'll have his reasons."
But he also reflected on his team's own shocking collapse, pinpointing Theo Walcott's goal at 4-1 at the end of the first half as decisive.
McDermott said: "The goal we conceded just before half-time was crucial, we've got to clear that and make sure it's 4-0.
"I wasn't comfortable at 4-1, I don't know why but I just had that feeling. They have got good players and they hurt us.
"What happened tonight was extraordinary, I've never seen anything like that from Reading at the Madejski Stadium."