Clough lost his job after four-and-a-half years at Pride Park with the club far from danger in 14th position in the Championship.
He was today unveiled as the new Blades boss and admitted that his dismissal in Derby upset him.
"I was disappointed and there was an element of anger there as well but we have to put that behind us," he told a press conference. "I am going to try and build a team here that is capable of challenging for promotion.
"I am looking forward to seeing the players at close quarters and things are slowly turning round. We have to be realistic, get out of the bottom four and go from there."
The 47-year-old takes over in South Yorkshire with the club currently in League One's drop zone on nine points from 13 games.