The Blades overturned a 1-0 half-time deficit to book a place in the quarter-finals as Nottingham Forest were beaten 3-1.
United will host either Sheffield Wednesday or Charlton Athletic in the last eight, the two clubs being due to meet a week tomorrow in a fifth-round tie that had to be postponed on Saturday due to Hillsborough being waterlogged.
Should the Owls triumph, that will mean Sheffield’s big two going head-to-head for the first time since February, 2012.
It would surely represent the biggest derby between the clubs since the 1993 FA Cup semi-final at Wembley which the Owls won 2-1.
Due to the demands of television, yesterday’s quarter-final draw took place around 40 minutes into the Blades’ tie against Forest.
It meant Clough, whose side were trailing to Jamie Paterson’s goal at the time, only discovered the identity of United’s potential quarter-final opponents once in the home dressing room.
He said: “We told the players (about the draw) just before we came out for the second half. I had ‘ummed and ahhed’ for a few seconds, but then I thought, ‘What the hell? Let’s tell them’.
“A few of the lads didn’t believe us. So, when we got back in after the second half I told them, ‘I was joking earlier, lads, we have got Brighton or Hull away in the quarter-final’.
“Seriously, though, I thought telling them might have a little effect. Every time we have approached a draw this season that is all people have been talking about – a Sheffield derby.
“It means a lot to people round here. That is the message we put out there to the players. You have 45 minutes to get the victory that could earn us a Sheffield derby.”
Elsewhere in the quarter-final draw, the winners of tonight’s fifth-round tie between Brighton & Hove Albion and Hull City will host Sunderland while in a re-run of last year’s final Manchester City will face Wigan Athletic.
Arsenal, 2-1 victors over Liverpool yesterday, will host Everton in the last eight over the weekend of March 8-9.
The draw means at least one non Premier League outfit will make it through to Wembley and after claiming another notable scalp in the form of Forest, few would bet against the Blades continuing to make a mockery of their poor form in League One by battling through to the national stadium.
Clough said: “Wembley is possibly 90 minutes away and, hopefully, they might pick us for television in the quarter-finals if it is the Sheffield derby.
“I believe our tie against Forest would have done justice to the TV. I thought our lads busted a gut. Their honesty shone through.”
There was one downside to yesterday’s celebrations at Bramall Lane with hundreds of home fans invading the pitch at the final whistle.
A smaller group had come on after each of the two late goals from Chris Porter which settled the tie.
The Football Association are likely to write to United about the invasions, especially the final one that saw Forest defender Jamaal Lascelles having to be led away by two team-mates as the elated home fans celebrated around him.
Referee Michael Oliver is, though, believed to have been relaxed about the matter and told United officials that they were down to “exuberance”.
Clough said: “I didn’t like to see the supporters coming on the pitch. I can understand the exuberance, but please try and stay off the pitch. I was a bit worried that one of the Forest players might react but, as far as I know, nothing happened.”
United’s progress to the quarter-finals will bring a headache in terms of fitting in the club’s remaining fixtures.
Even before seeing off Forest, the Blades did not have a blank midweek until April 8 and now the home derby with Rotherham United – scheduled for sixth-round weekend – will have to be found a new date.
Clough’s side return to league action on Wednesday at Gillingham and he admits the club’s schedule will bring a few headaches.
He said: “We have a bit of a problem with fixtures. Rotherham will now have to go into April, but it is a nice problem to have.
“The Cup is great but we need points on the board.
“We have to get out of that bottom four.
“We have to forget about the FA Cup now. It is great that we have a few more quid in the coffers.
“But what is far more important is the next three games in the league. Gillingham, Bristol City and Colchester are our priority before we can think about the FA Cup again.
“The atmosphere against Forest was incredible. I said to the players afterwards, ‘That is the sort of atmosphere we want to play in every week – and if we can get a successful side on the pitch, I would imagine it would be like that every week’.
“Everything was great but we won’t get that in League Two. We have to get out of trouble.”
Blades’ endeavours get deserved reward: Page 4.