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."

Irish slipped back to the foot of the table after defeat at Sale and Newcastle's win against Harlequins.
The Exiles host 10th-placed Worcester on Sunday and could move above the Warriors with a win.
"We've already spoken about next week and what we need to do," Coventry told BBC Radio Berkshire.
"The boys have had a bit of a hurry up in the changing room. We've spoken about how disappointed we were with our second half performance (at Sale)."
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Irish conceded 26 unanswered points in the second half as Sale ran in a total of six tries at the AJ Bell Stadium.
It was the second time in their last three Premiership matches Irish failed to score any second-half points.
And following news that prop Ben Franks will be ruled out until late April with a ruptured bicep tendon, Irish have been hit by a further injury to winger Alex Lewington.
The 24-year-old is expected to be sidelined for up to six weeks following surgery on a fractured thumb.
"Injuries are a big part of the game, we have to rely pretty much on the squad that we've got," Coventry added.
"We can't lament our losses too much, we have to get on with it.
"Losing Ben and Alex is a frustration, but we'll just have to manage without out them until we can get them back on the field."

Wimbledon mixed doubles star Jamie Murray said he would not mind if his brother chose someone else for the task.
Jamie told the BBC: "If I don't get asked that's absolutely fine by me."
Wimbledon singles champion Andy announced his engagement to girlfriend Kim Sears in November last year.
In an interview with BBC Scotland Sport, Jamie said: "I haven't been asked yet so I'm still waiting on that one.
"We'll see. If I get asked: great. If not, then it's not the end of the world.
"I'm sure it'll be a good day."
Jamie said he was hoping to avoid having to do a speech even if he is asked to take on the post, having allowed Andy to forgo the tradition at his marriage to Alejandra Gutierrez in 2010.
"He was best man at my wedding," Jamie said. "And I told him he didn't have to do a speech because I didn't want him to be stressed right through the day and not be able to enjoy it.
"I could do a speech if he wants me to, but I'm not going to be sticking my hand up for the front of the queue."
While few details of plans for the wedding have been revealed publicly, mother Judy Murray told the Mirror the wedding would be held in October, but said she didn't know if it would be in Scotland.
Manager Steve McClaren praised Derby County's control as they came from behind to knock Premier League West Brom out of the FA Cup.
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London Irish head coach Tom Coventry admits their meeting with fellow Premiership strugglers Worcester will be a "huge" game for his team.
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Andy Murray is getting married later this year but his older brother said that, so far, he has not been asked to take on the role of best man.