McClaren was installed as Nigel Clough's replacement ahead of the match against Ipswich but only watched from the stands as the Rams rallied from a 4-1 half-time deficit to draw 4-4.
He then took charge of his first game at home to Leeds, overseeing a first home win of the campaign as Leeds were put to the sword 3-1 at Pride Park.
"To score plenty of goals bodes well for the future and it's nice we've had them coming from different players as well," McClaren told the club website.
"Putting the ball in the net is never easy in football so you can't fail to be impressed by what the players have done.
"I knew that the team could score goals anyway but the quality of them has been outstanding and that's what I like to see."
Next up for McClaren's men following the two-week international break is a trip to Watford on Saturday.