Scottish winger Ryan Flynn and on-loan Derby County defender John Brayford scored second-half goals in the space of two minutes to secure United a place in the last four for the first time since 2003.
Clough arrived at Bramall Lane in October not long after being sacked by Derby, with the club lying second from bottom in Sky Bet League 1. A 2-0 victory over Peterborough last Tuesday was their eighth straight win in all competitions - they are now 11th - and a ninth consecutive victory yesterday has ensured they become the first club from the third tier to reach the semi-finals of the competition since Wycombe Wanderers in 2001.
"There's not an awful lot of satisfaction for me personally," said Clough. "I don't have a chart at home where you rank the games. I don't honestly, it's not about that. It's about the players and supporters, especially this, celebrating together."
United have beaten Aston Villa, Fulham and Nottingham Forest in previous rounds and the momentum was clearly with them in front of a sell-out Bramall Lane crowd of 30,040.
Charlton, though, gave as good as they got before the game's turning point in the second half: winger Callum Harriott spurned a golden chance to put the Londoners ahead, dragging his 10-yard shot wide from in front of goal.
"We were nervous in the first 20 minutes and it was important to get in 0-0 at half-time," Clough added. "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.
"We're going to try [to win the trophy].You look at the teams left in and it's a little bit scary. But we're not going there for a day out. You go to the seaside for a day out, not to Wembley."