He told the club's official website: "There are no excuses for what I did and I'm sorry for my reaction. I was out of order, but nothing like that has ever happened to me before and I was wrong. I've been around the game long enough to know that shouldn't happen.
"I feel like I've let a lot of people down - Brian especially. He was the person who put me in the team and gave me a run of games. He's the one who gave me the captain's armband, which was a massive goal of mine when I joined Reading. Now the only way I can repay him is to keep performing for him.
"It's a massive honour to represent Reading and to react how I did doesn't put myself nor the club in a good light. So I just want to apologise to the fans, the club and everybody here."
McDermott added: "We have taken disciplinary measures and Matt is fully accepting of mine and the club's position. Now we can move forward."