Tom Ince and Darren Bent struck inside four second-half minutes to record the Rams' first FA Cup victory over a higher tier side since 1986 and seal a 2-1 win.
They cancelled out Matt Phillips' opener to surprise the Premier League club and secure Derby's first triumph over a top-flight team for eight years.
McClaren's side have lost just once in their last 12 games and are also seventh in the Sky Bet Championship, and the manager was delighted with their efforts at The Hawthorns
He said: "You've got to perform to come here and win
You've got to fight and show character and you've got to stand up, and the team did that
It was a fantastic reaction after Monday (a 3-0 defeat at Norwich).
"That's what we asked for in terms of performance
The bonus was the result as well
There were some heroic performances out there.
"The performance, fight and character was excellent and the bonus was the result."
Ince scored his ninth goal of the season when he deceived Boaz Myhill with a free-kick and McClaren urged the wideman to maintain his form.
"He has got to keep that going
It is consistency, it is doing it week in and week out, day in and day out, and being relentless, just keep going, keep going," said the ex-England boss.
"That is what he has done
He has got great ability and can finish and score
I don't tell him anything we don't tell other players
Maybe the response is better
"We just allow him to go and play and he does the work as well, up and down, he has got great fitness and he should be a Premier League player."
Craig Dawson hit the post for Albion and Richard Keogh cleared off the line from Salomon Rondon early on but the Baggies never recovered from falling behind
Scott Carson tipped Rondon's injury-time header over as Albion were dumped out of the cup by a Sky Bet Championship side for the second straight season following defeat to Reading last year
Boss Tony Pulis said: " I didn't see it coming, even after they scored their goals
The two goals are disappointing
I still thought we did enough to not get beat today
"I thought we battered them at times
We got in 60 crosses today, had nearly 30 shots
I'm not sure how many were on target
All the stats show we've had a right go today
"In cup football you need the breaks and a bit of luck
Derby defended heroically, you can't take that away from them
We're really disappointed because the players have played well and given it everything."
Source : PA