The Rams dominated for long spells of the match, but were forced to wait for two second-half goals to book their spot in the fourth round of the competition, and McClaren was quick to praise his players.
"We have spoke about discipline and concentration and the team had that tonight," the former England manager told reporters. "We got the clean sheet and if we keep doing that we will win games.
"We have got players who are dangerous, can create and can score goals. We had to stay patient, but in the end it paid off.
"Reading are a good team and we knew it was going to be tough. But even though we made six changes, we felt the team was good enough to win, and it did."
Derby return to Championship action against Bolton Wanderers on Saturday afternoon.