Stags began in thrilling fashion but soon tired as the exertions of Saturday's superb FA Cup display at Doncaster caught up with them while Storm Barra blew through the ground to make life even harder.
“In the context of having our three best strikers out plus no skipper and seven players out, that was as good a three points as we've had all season,” said Clough.
“You have to do whatever you can to win a game, they are all different.
“Sometimes you have to scrap and fight. Tonight we were not at our best and gave the ball away to easily. But we got the three points and a clean sheet.
“The win was unbelievably hard-earned on the back of Saturday.
“We started the game very well indeed for the first 20-30 minutes, then I think we ran out of a bit of energy and legs.
“They got into the game 10 minutes before half-time and continued it throughout the second half.”
He added: “Although we had a couple of situations it was more about protecting our clean sheer and that 1-0 lead which, apart from hitting the bar with that unbelievable effort, I thought we did exceptionally well on low energy levels tonight.
“They came and played exceptionally well. They are a good footballing side and Callum Guy is one of the best midfielders in the division.
“But Bish has not had too many saves to make tonight and we made them work hard for anything they got.”
Rhys Oates (dead leg) and Ollie Clarke (calf) both missed out injured and are doubtful for Saturday's visit of Salford City.