The Rams endured a nervy end to the game as Rudy Gestede made it 3-2 with 12 minutes remaining, but the former England boss said that it would have been a "travesty" if the hosts had equalised.
"That is always evident - they showed it on Sunday [against Nottingham Forest] and we had to show it again but in a different way," Sky Sports News quotes McClaren as saying.
"I think we deserved the result; it would have been a travesty if they had equalised. Last year we drew this game against Birmingham 3-3 when 3-1 up but we've hung on and got the point and it's a big win."
The result moves Derby up to seventh place in the table, while Rovers remain in 13th.