United were 1-0 down at half-time in Sunday's FA Cup fifth round tie, following Jamie Paterson's opener for Forest, but Conor Coady equalised, before two injury-time goals from ex-Derby County man Chris Porter completed the turnaround.
The quarter-final draw, which was made during the first half of United's game, pitted the tie's victor against the winner of Sheffield Wednesday versus Charlton Athletic
And Clough revealed how the news of a potential derby clash in the next round helped fire his players up.
He told BBC Radio Sheffield: "We told (the players about the quarter final draw). Just before we went out (for the second half).
"A few didn’t believe us actually,” he added. "We just had a laugh with them at the end of the game and said 'no, we were joking, it's Brighton and Hove away'."
United's heroic effort was underlined by the fact that defeat for Forest was their first in 16 games.
However, the former Derby boss was quick to highlight the importance of his players retaining focus on their league campaign, despite a cup run that has seen them eliminate Premier League pair Aston Villa and Fulham.
"We've beaten an exceptionally good team who are going to be challenging for automatic promotion," Clough added.
"Sixteen games unbeaten is a long time and for us to end (the run) in the manner that we did was brilliant."
"I'm looking forward to it, but far more important are the next three league matches: Gillingham, Bristol City and Colchester, they will take priority over everything.
"(The cup run is) brilliant, it puts a few more quid in the coffers but those three league games are far more important."
