Theo Robinson reduced the deficit for the Rams after goals from Zak Whitbread and Martyn Waghorn had given the home side a two-goal lead.
But David Nugent came off the bench to score twice more in the second half to condemn Derby to defeat and a fifth successive league loss to Leicester.
"The first time Cardiff went in our box the other night they scored and it was the same with Leicester. It's another goal conceded from a set-play," said Clough.
"That's the only thing that's holding us back. The general performance was not too bad for long periods of the game.
"But all that goes out the window if you don't defend properly and we certainly didn't in the first half hour.
"If you give someone like Leicester the first goal after five minutes they're going to be all over you. They're extremely strong at home."