Clough will be in charge of the Rams by the second-leg after watching tonight's contest from the stands.
His father Brian won the competition four times with Nottingham Forest, so it is remarkable Clough should find himself just 90 minutes away from a final - almost certainly against Tottenham - himself.
Ferguson does not know whether Clough's emotional appointment had an impact on Derby's performance.
However, he has been around long enough to know what a galvanising effect a new manager can have.
"It happens so many times historically, there is no rhyme or reason to it," he said.
"A few years ago we played West Ham and Alan Curbishley had just taken over and they beat us 1-0. It is a strange thing."