Dickov provided the assists for both goals. His diagonal cross into the box four minutes after the restart was brilliantly cushioned on the chest by Hulse, who then flicked the falling ball beyond keeper Dimi Konstantopoulos.
Dickov then retrieved Stephen Pearson's cross to tee up Hulse for a crisp first-time finish after 62 minutes.
"(Hulse) went down the Thursday before the Ipswich game and was laid low for about four days, but he's trained most of this week and he looked pretty strong," said Clough.
"They were two very good goals. We haven't given him too much service in the last few weeks when he has played, but tonight we did and he looked dangerous all night - as did Paul Dickov, who I'm sure Rob was first to thank for his goals."
Hulse could have had a hat-trick but his late penalty was saved by Konstantopoulos diving to his left.
Clough revealed: "He changed his mind as usually he goes the other way.
"It's not so bad when you miss them and they don't cost you points but he's disappointed because it would have been for a hat-trick."
Coventry finished the game with 10 men after Jordan Clarke was sent off in the 63rd minute.
The young defender received a second yellow card for bringing down Robbie Savage. He had been booked in the first half for mistiming a challenge on Dean Moxey.
However, despite the red card, City boss Chris Coleman was impressed by Clarke and felt the 17-year-old's dismissal was harsh.
"Jordan Clarke had a very good game," said the Welshman. "He's only a baby out of the academy. He's inexperienced but he coped very well I thought.
"As for the red card, both players went in. Jordan is already on a yellow card but he's a full-blooded player and a tough defender - he's not a dirty player - and he was never going to pull out of that challenge.
"I'm not going to say I will need to see it again, but what I will say is that we had one referee in the first half and another in the second half.
"Derby are at home and their supporters got excited about the challenge, when that happened I knew there was only going to be one outcome."
Coventry go into the international break on the back of four defeats in their last five league games.
Coleman believes the two-week sabbatical will benefit his side and he hopes to have some players back from injury when they resume Championship action at home to Crystal Palace on November 21.
"The break will do us good, to get away from things and each other for a while," Coleman said.
"We should have Stephen Wright back while Keiren Westwood and Ben Turner will hopefully be back as well.
"James McPake will need to go on loan to get some games to build up his match fitness."