The Blades booked a spot in the last four and a day out at Wembley on Sunday as they overcame Charlton Athletic 2-0 at Bramall Lane - courtesy of second-half goals from Ryan Flynn and John Brayford.
Clough's men, who have already seen off Aston Villa, Fulham and Nottingham Forest in this season's competition, will now meet Hull City at the home of English football.
They will be sure to make the most of that occasion having defied the odds to become the first third tier side to reach the semi-final stage since Wycombe Wanderers in 2001.
Clough said of the victory over Charlton, which came in front of a sell-out 30,000 crowd: "We were nervous in the first 20 minutes and it was important to get in 0-0 at half-time.
"The atmosphere, it saps you when you're not used to it and a lot of players playing in this sort of thing for the first time, this atmosphere takes your energy and it takes your breath away at times.
"To get to this stage as a League One club in the semi-final is an incredible achievement.
"No easy draws as well along the way, going down to Fulham and Villa Park, and we've had a few breaks like here when the lad missed that chance (Callum Harriott firing wide shortly before the deadlock was broken).
"It's essential that you get that little break at certain times."
When pressed on how United's season has been turned around, with the Blades having now won nine on the bounce, Clough added: "Hard work. The work-rate of the players.
"We had a sit down after the Crewe game, which was February 1. We lost 3-0 and were awful that day and we had a bit of a clear-the-air, went down to Fulham and won and we've gone on from that point."
With United now looking up rather than down in League One, Clough insists they will make a first trip to Wembley in the FA Cup since 1993 determined to keep a fairytale run going.
He said: "We're going to try (and win it).
"You look at the teams left in and it's a little bit scary, but it's about the financial boost and everybody enjoying Wembley.
"But we're not going there for a day out. You go to the seaside for a day out, not to Wembley."