McDermott was dismissed by Royals owner Anton Zingarevich earlier this month with the club deep in the relegation mire, and former Southampton boss Nigel Adkins has since been appointed as his replacement.
Many of the Reading squad were reported to be shocked by the decision to sack McDermott, and the former Royals boss has revealed he was as surprised as anyone by the news.
"It was initially very difficult, but everyone has to move on and you get on with it," McDermott told Sky Sports. "It was a shock, because I've been there 13 years and loved every second.
"I had a phone call on the Saturday to see the owner on the Monday and didn’t think too much of it, I thought it was just to discuss the team [to play] against [Manchester] United.
"The owner wanted to see me at 3 and I didn’t think too much of it. It wasn’t normal but just I didn’t get it, until I went into the room and thought 'This guy is going to sack me.'
"It was difficult for him. He made his choice and his decision. I can’t say I agree with it, but I’ll never have a problem with Reading as a club. He thinks what he’s doing is right.
"It’s about the next challenge for me now. I was hungry before, and I’m hungrier now.
"I thought I’d be there forever - that’s how you think - but the club is going in a different direction and I think Nigel Adkins is a superb guy and a superb manager."
McDermott also admitted his surprise at hearing the news that Sunderland boss Martin O'Neill has also been dismissed after a run of poor results.
"It’s a surprise about Martin," McDermott said. "He left a message on my phone when I was sacked. With seven games to go it’s difficult to go in there and make a difference.
"When you consider the experience and expertise Martin brings it’s a big, big decision. Sunderland must have someone lined up to take over almost immediately. I’d be very surprised if they haven’t."