The Blades played their part in an incredible semi-final second leg at the County Ground, with the Blades staging a dramatic late rally from 5-3 down on the night and 7-4 in arrears on aggregate to score two late goals and pile the pressure on the Robins with Matt Done and Che Adams netting.
But despite having to negotiate around eight minutes of stoppage-time, the Wiltshire outfit held on to book their place in the play-off final against Preston at Wembley after the second leg ended 5-5 - with Swindon winning through 7-6 on aggregate.
It represented the Blades’ ninth failure in the end-of-season lottery.
For Clough, it was play-off heartache once again after some previous woes at Burton, but the former Derby boss was heartened with the way his side kept going before eventually just falling short.
Clough said: “In the first 15 minutes it could have been 3-3, but they put their chances away and we didn’t.
“The fact we were still going in the 97th and 98th minutes was encouraging.
“You cannot describe how disappointed we are.”
For Swindon boss Mark Cooper, it was a roller-coaster evening, but fortunately for him, the right outcome.
His side had been 3-0 in front after 18 minutes and 5-3 after 84 up, but United scored two late goals to set up a nervy finish.
“I can’t put into words what I’ve just seen to be honest,” said Wakefield-born Cooper, son of Leeds legend Terry.
“I’m putting it down to being a freak of a game, I don’t think there will ever be another one like that.
“It was like two heavyweight boxers trying to knock each other out.”
The result set a new record for the highest number of goals in a play-off semi-final.