The Royals looked to be heading for defeat when Romelu Lukaku added his second goal after the break, but Jimmy Kebe's strike sparked a thrilling fightback.
Adam Le Fondre levelled from the spot with two minutes remaining before Pavel Pogrebnyak pounced in stoppage time to claim a precious win for Reading.
McDermott said: "You have to believe in the players that we've got. I think the crowd here, they don't know how important to us they really are. They got us over the line here today.
"Once we scored the goal, the Jimmy Kebe goal, they really got into the game and made a massive difference to our players.
"Then when we scored to make it 2-2, I thought I don't want to lose this game, but we might as well try and win it because it was so important and I think Pavel Pogrebnyak's finish was top drawer for the third goal.
"I'm looking forward to watching the last eight minutes of that game."
McDermott admitted his side had to produce a much improved second-half display after letting West Brom get a grip on the game.
"Yeah it was flat for whatever reason," he said. "We couldn't really get beyond our striker, they looked pretty comfortable West Brom and you know Steve Clarke's done a fantastic job there.
"They will be disappointed to be two up and lose the game I know that, but all I can say was our side was really resillient.
"I've been lucky enough to work with these guys for a long time now and they've got great character."