The Rams were undone by an early Jordan Rhodes penalty before Scott Dann headed a second deep into first-half injury time, which Clough felt went on for too long.
He said afterwards: "We conceded the killer second in disputed added time I have to say. He put a minute up and it was two minutes 25 seconds when they added the second which we just wondered what happened. We didn't see a stoppage.
"We certainly paid for our failures in both penalty areas. We spent the last couple of days chatting about keeping Blackburn quiet. To give the penalty away how we did was amateurish. It gave Blackburn a big lift and then we create three as good a chances as you'll get away from home."
Clough also bemoaned the referee's failure to award a penalty when Morten Gamst Pedersen appeared to bring down Ben Davies, adding: "Even if the penalty had have been given on Ben Davies, which was pretty blatant, then you never know. It would have created a nervy situation for Blackburn."