Jamie Ward and Craig Bryson netted the goals which consigned Charlton to a fifth successive defeat - but McClaren admitted it was not an easy task.
He said: "For the first 20 minutes we could not get hold of the ball. We showed resilience at the right times to defend resolutely and keep a clean sheet. We also showed we can score goals at the right time as well."
The Derby boss has lost just once in the 11 games he has been in charge since taking over from Nigel Clough, including the 4-4 draw with Ipswich, and has overseen eight wins, so believes he knows what it takes to do well in the Sky Bet Championship.
He explained: "You have to win in different ways in the Championship. We showed that in the way we scrapped to get the three points from a very difficult game.
"There are 46 games in this league and we are not going to be playing the same. That was a completely different way of playing than we did the week before at Blackpool."
Ward scored in the 32nd minute with a deflected free-kick, before Bryson - who had hit the crossbar - wrapped things up three minutes from time.
As happy as McClaren was with the goals - Derby have the most in the Championship with 42 - it was the clean sheet he was most pleased with.
He said: "It was all about keeping the clean sheet. We know we can score goals, we have demonstrated that."
Despondent Chris Powell found the fifth defeat in a row difficult to take.
"I felt we got our shape and tactics right for half an hour before they scored with a deflected goal," said the Addicks boss.
"They then had the impetus. Ben (Alnwick) made a great save to keep us in it at 1-0. We needed something to break the cycle but it just didn't happen."
Powell rued a headed miss by skipper Michael Morrison and Simon Church had a good effort well saved by Lee Grant.
He said: "Given how effective he usually is in the opposition box, 99 per cent of the time he would score with that header.
"Then Simon Church has a chance when we are chasing it but it doesn't go in. We conceded a breakaway goal but that was us going for it."
With the season approaching the halfway point Charlton hover fourth from bottom in the table.
Powell said: "We know we are in a dogfight. The reality is we are where we are and have to get on with it. It is a tough one to take."