Noel Hunt's second-half header from a Kebe cross was enough to secure an eighth win in 10 games for the Royals and send Derby crashing to a first league defeat at Pride Park since late November.
McDermott was happy with a composed display from his side and said: "It was efficient and we needed a little bit of Jimmy Kebe to make the goal for us.
"Derby worked really hard on him, but we felt he has always got that bit of quality to make the difference and he's produced a good cross and Noel's got in a good header and we're happy.
"Noel has worked hard and so has Jason (Roberts) as the strikers have to away from home, but the whole team did. I thought we looked solid and disciplined as we had to be to come to a place like this and get a result."
Reading are now inside the top six and hoping their form can carry them through to the play-offs and McDermott added: "Eight wins from 10 speaks for itself. We normally leave it until end of March or April so we're happy enough."