The Championship Rams turned a one-goal half-time deficit into a 2-1 victory to book a place in the fourth round.
McClaren told BBC Radio Derby: "We told them to keep their composure We were causing them problems and controlling the game.
"How the players kept their composure and came back, credit to them."
Darren Bent and Tom Ince scored goals three minutes apart in response to Matt Phillips putting the hosts ahead in the first half.
And McClaren was keen to point out the contribution of a massive following from Derby.
"I had heard 6,000 were coming along and they were going to fill behind the goal," continued McClaren.
"We said to the players that it's a cup tie and there's 6,000 fans coming to watch, so there's a reason why we've got to fight, we've got to react and come back.
"I'm so pleased for the players, I'm so pleased for the fans and very proud of them."
Manager Steve McClaren praised Derby County's control as they came from behind to knock Premier League West Brom out of the FA Cup.