Ian Harte, enjoying an Indian summer at the Madejski Stadium, scored his 13th goal of the season from the spot to open the scoring, but Jamie Ward equalised from Derby`s first real chance.
Daniel Ayala, who had brought down Simon Church for Reading's opener, then fouled Michail Antonio in the area for a second penalty, but this time Harte hit the post from 12 yards. They were not to be denied, though, and a scruffy strike from Hal Robson-Kanu after 72 minutes secured a deserved victory.
McDermott, who is now looking forward to tackling Cardiff in the play-offs, said: "The most important thing was to win going into the play-offs. Derby played well but we missed chances.
"Ian Harte missed a penalty and I would I fancy Ian to take penalties anywhere in the world. The win is the most important thing. We are right in the mix and now in the semi-finals of a cup competition.
"I had a funny feeling we would play Cardiff. Both our games this season were draws and there was nothing in it. I just wanted to get into the play-offs. Whoever we were going to play is not an issue. Over the past 17 games we are top of this league and over 28 games we are second, so our form is as good as anybody's. Now we have just got to prepare the players and get ourselves ready."
Source: PA
Source: PA