QPR's Bobby Zamora pounced on the error to score the winner and secure the club's promotion back to the Premier League at the first time of asking.
"I can't remember what Harry [Redknapp] said at the end. I was in shock," McClaren told reporters.
"Football is a cruel game. One lapse and you lose a game like that. It is going to take a few days wallowing in our misery before we recover.
"We stayed on the pitch to watch QPR pick up the cup. It does hurt but we said we don't want this hurt again."
Derby finished the regular season in third place.