Their 10-game unbeaten Championship run came to an end at Carrow Road and McClaren wants new players to help them climb into the play-off places.
"The squad has been tested over the last couple of weeks," McClaren told BBC Radio Derby.
"We were a little bit short [against Norwich]. It was one game too many."
A bid has already been submitted for Nottingham Forest captain Henri Lansbury, and Derby are still interested in the midfielder.
McClaren is also still hopeful of bringing back Chris Martin from his loan spell at Fulham - despite the London side's reluctance to release the striker.
Injuries to left-backs Craig Forsyth, Marcus Olsson and Max Lowe - plus makeshift left-back Ikechi Anya - mean the Rams are also in need of more defensive cover.
Former England manager McClaren, whose side are in seventh place and just two points outside the top six, told BBC Radio Derby that a bid for Lansbury had been made.
"They have turned it down and we will discuss that even further," he added. "He is a player we have always admired but I will leave it to the club and see if anything can be sorted.
"That [Martin deal] is at board level at both clubs. They made an agreement to do the loan and if it needs to be terminated they need to make a decision to do that."
BBC Radio Derby's Owen Bradley
Derby's 10-match unbeaten put the Rams firmly back in the Championship promotion race, but the view within the club and amongst supporters is that new signings in January will be needed to keep them there.
Steve McClaren had already made a move for Nottingham Forest captain Henri Lansbury before the defeat at Norwich, though that result and performance underlined why they need some new blood. Derby also hope that Chris Martin will return early from his loan spell at Fulham, with McClaren desperate to be reunited with his former top-scorer at Pride Park.
That won't be the end of it for Derby, even if they are able to land their top two targets. McClaren might decide to bring in a defender following yet another injury, and will almost certainly look to exploit the loan market as he did so effectively in his first spell in charge.
Expect the Rams to be busy between now and the end of the month.
Derby County boss Steve McClaren says the 3-0 defeat against Norwich City showed how important it is for the Rams to strengthen their squad in January.