Faz Rawson and Oli Hawkins were ruled out with illness while Stephen McLaughlin was injured in the first half.
But two goals from George Lapslie and one from Will Forrester saw Stags come from behind and then, after conceding a late second, hold out for a place in the prestigious third round draw.
“With Stephen McLaughlin going off that was eight players we were without today – five or six defenders and our two main strikers,” said Clough.
“In that context it's even a better result.
“Faz Rawson got a bit of food poisoning or something on Wednesday that wiped him out.
“Oli Hawkins has got a bit of this flu that's going around. He didn't train Wednesday, came in Friday and did a little bit, and then woke up this morning not feeling great at all.
“We had a team picked yesterday. That changed at lunchtime when we lost Oli Hawkins. We started with a formation, changed it halfway through the first half and then again at half-time.”
On the game, itself, Clough added: “I am relieved as I was a bit frustrated at half-time with the way we had performed
“But from kick off in the second half, the second 45 was as good as we've been for a while
“I thought we controlled the first half completely but conceded an unbelievably poor goal. We then controlled the game without having any efforts on goal.
“We had a little chat at half-time and got things sorted in the second half.
“We lost Oli Hawkins about half 11 this morning, then to lose Macca at half-time we had to change it round a little bit
“It probably helped us as I don't think in normal circumstances we'd been using Jordan Bowery and George Lapslie as wing backs.”
Forrester's equaliser came just after half-time and Clough said: “Timings of goals are very important and to get one back straight away didn't give them time to settle.
“Don't underestimate the significance of us kicking towards our fans in the second half either - it makes a hell of a difference. I think they enjoyed it and we did too.”
Stags' third was a great team goal and Clough said: “That third goal is one that anyone who watches us training knows, we score goals like that in training quite often and at last we've put one in during a game.
“I hope it gives us the confidence to play more stuff like that and score more goals like that as it was a brilliant effort.”
Stags saw out the five added minutes without mishap and Clough said:
“We kept the ball and almost scored a fourth ourselves.
“Be nice and solid but don't stop looking for that fourth goal. We had one or two situations at their end and we generally kept the ball away from our goal.
“The only one disappointed in there is Nathan Bishop as the ratio of goals he is conceding at the moment to the number of shots he is having is incredibly harsh.
“I'm not sure how he's not keeping clean sheets. Whenever the opposition have an effort it's ending up in the back of our net.”
The third round draw is on Monday night and Clough added: “We are due a home draw so we will take anyone at home.
“You either want one that gives you a chance of getting through to the fourth round or you take the glory.
“It would be nice for our fans to be at home and not have to go anywhere and let's have a good day in January at the One Call.”