O'Driscoll, who was appointed manager of the Rams' npower Championship rivals Bristol City this week, was surprisingly sacked by Forest on Boxing Day following a 4-2 home win over Leeds which left the Reds a point shy of the play-off places.
The ex-Forest coach had only been in charge since July after being brought back to the City Ground by the Al Hasawi family following their takeover of the club.
Ahead of the east midlands derby at Pride Park on Saturday, Clough said: "I sat with Sean O'Driscoll at Birmingham on Tuesday night. He said he was disappointed about what happened at Forest.
"I don't really like to comment on other clubs, but from a personal point of view what happened to Sean was harsh. But he's got another chance now at Bristol City and that's great for him."
Former Forest striker Clough added: "Unfortunately at many clubs there seems to be this instant demand for success, but football doesn't work out like that."