Clough, who was the longest-serving manager in the Championship, was relieved of his duties following a 1-0 defeat at the City Ground.
Darren Wassall has been placed in temporary charge of first-team affairs after four of Clough's coaching staff were placed on gardening leave.
The Derby board has told Andy Garner, Gary Crosby, Johnny Metgod and Martin Taylor to stay away from the club.
Clough's brother Simon, who was appointed chief scout at the beginning of 2011, has also been placed on gardening leave.
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