Supporters also booed when McDermott took off Noel Hunt as the Royals slumped to their fifth straight defeat - four of them in the Premier League.
The Reading manager said: "That is unusual. But it's their prerogative.
"Frankly, I was gutted for Mikele, because I know what a good guy he is and how good he has been for us over a long period of time.
"I'm bitterly disappointed for the fans and players. But I'm strong. So are the players. They're winners."