The Royals boss replaced Leigertwood with Danny Guthrie for the closing stages of Saturday's 2-1 defeat at home to Aston Villa.
McDermott says he felt sorry for Leigertwood as the fans responded positively to his departure, while the Madejski Stadium faithful also booed when Noel Hunt was taken off.
"That is unusual. But it's their prerogative," McDermott said in The Sun.
"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."
Reading's defeat left them in the relegation zone and four points adrift of safety ahead of their next game against Manchester United, but McDermott is staying confident about his side's chances of beating the drop.
He said: "I'm bitterly disappointed for the fans and players. But I'm strong. So are the players. They're winners."