McDermott, who joined the club during Magpies' boss Alan Pardew's reign at the Madejski, saw his side fall behind to Yohan Cabaye's first-half opener.
But Adam Le Fondre climbed off the bench to score two late goals and give Reading three vital points, seven days on from their come-from-behind FA Cup victory over Crawley.
McDermott said: "Adam Federici pulled off a couple of really good saves in the first half which proved to be match-winning saves.
"Pavel Pogrebnyak had a real chance in the first half before they scored and we could have been 1-0 up.
"But you come here and they get to 1-0 up and then it's never going to be easy.
"But I thought in the second half, we upped our game.
"You have to manage games. You have to stay in the game and once Newcastle didn't get a second goal, we knew we were in with a shout the longer the game went on."