After Stoke defender Robert Huth had opened the scoring with a 67th-minute header, a fierce strike from substitute Cameron Jerome with nine minutes of normal time remaining appeared to make three points safe for the hosts.
But Adrian Mariappa nodded in two minutes later for the Royals, who had scored a host of important late goals in their recent unbeaten sequence of four league games.
Reading might have completed another dramatic comeback if referee Michael Oliver had not waved away Adam Le Fondre's penalty appeals late on.
McDermott had no doubt what he thought about the penalty claim.
"Once we got to 2-1, I thought we would get it (a draw), and unfortunately the ref has missed a penalty at the end, the last kick of the game," McDermott said.
"He got hold of the ball, flicked it by him and he caught him. It was a stonewall penalty. I've just gone in to see him (Oliver) and he didn't see it that way, so that's fine, but I thought it was.
"Sometimes as a manager you get those things - with the last kick of the game, it would have been great to get the point.
"We hung in there and showed great resilience and desire. This is not an easy place to come to, which everyone knows."
Reading remain 17th in the table, two points clear of the relegation zone, while Stoke stay 10th.