A thunderous 30-yard drive into the roof of the net from left-back Joe Jacobson set up Shrewsbury for a 2-0 win over the Blades.
Jacobson took aim from outside the box to fire the Shrews into a 39th-minute lead and, after he limped off with a hamstring injury, it was left to substitute Liam McAlinden to seal only a third win of the season for Graham Turner's team with an emphatic second goal 10 minutes from time.
It was a loss for Clough in just his second game in charge and his side found chances hard to come by.
There were signs the Blades were in the mood to make a game of it when they started the second half brightly but then Febian Brandy, introduced by Clough at the break, was sent off for shoving Shrewsbury defender Goldson in the face.
Clough said: "Once you raise your hand you can have no complaints. His ill-discipline's maybe cost us a point or three."
Despite the result Clough was not too disheartened, he added: "I thought the attitude was excellent, the effort that went in. I thought we kept plugging away with 10 men at 1-0 down. We created chances.
"We saw a lot of good things out there. I said to George Long he's had two shots to save in the whole game. Even with 10 men we were in control at times and pressing for the equaliser until the second goal went in.
"We had a lot of possession in and around their penalty area but there was just a bit of quality lacking in the final third, the final delivery."