Jack Hobbs's lone goal for Forest at the City Ground on Saturday meant the Rams slipped to a third loss in eight days and the club confirmed in the evening that Clough had paid with his job.
The former Burton boss, who followed in his late father Brian's footsteps when he took the Derby job in January 2009, had been the fourth longest-serving manager in English football.
A club statement read: "The club would like to place on record their thanks to him for his tireless efforts to bring stability to Derby County, and his hard work and dedication throughout his tenure.
"However, after much consideration, the board feel it is time to move Derby County forward to the next level, which will necessitate a comprehensive review of the club's football operations.
"The ownership group remain steadfastly committed to the club and maintain their desire to compete at the top end of the Championship this season.
"The search is well underway to identifying and appointing a successor, and further announcements will be made in due course."
Clough, who leaves Derby 14th in the Championship, had earlier taken positives from his side's performance at the City Ground.
"We are pleased with a lot of things we did, just not the result," he said.
"We are not getting away with the mistakes we are making and a lot in the opposition penalty area is not going our way either - and we are certainly not getting a lot of breaks from the officials."