The former England boss suffered his first loss since taking charge of the Rams, with a strike from Jermaine Jenas and a Jake Buxton own goal either side of a Simon Dawkins equaliser inflicting the damage.
Nevertheless, McClaren, who worked as a first-team coach with the West London outfit prior to replacing Nigel Clough at Pride Park, has no complaints over the defeat, claiming his side lost to the strongest team in the Championship.
Speaking to his club's official website, he said: "I'm proud of the players. They had a right go against the best side in the division this afternoon."
However, the 52-year-old was disappointed by the manner in which the winning goal was conceded, claiming there is room for improvement in combating set pieces.
"To lose to a set play is so disappointing," he added. "It's an area in which we can improve in because we've conceded too many like that."
Harry Redknapp's men kept to within two points of table-toppers Burnley following the victory.
Derby, who sit 11th in England's second tier, host Sheffield Wednesday at Pride Park next Saturday.