Lucas Akins' late penalty earned a 2-2 draw before Christy Pym saved two spot kicks against his former club in a 3-1 shoot-out win to reach round four for the first time since 1975.
“We are into the next round for the first time in nearly 50 years which is a hell of an achievement, but so is going 12 games unbeaten,” said Clough.
“For quite long spells we were second best as they were so good. There wasn't too much we were doing wrong. They were just very competent.
“The respect they showed us by naming a full side said everything.
“They are a top side in League One and you can see the big difference – the pace and the speed they move the ball. We just hung on in there.
“It was very important for Will Swan to get his first goal of the season and there were no complaints from their players over the two penalties so the referee was spot on with those.
“We could not play out as much as they were literally putting up everybody man to man against us. And we didn't want to concede silly goals when they were so good.
“The free kick we conceded was a bit soft. I think the movement on the ball just deceived Christy Pym and he was a bit disappointed with it at half-time. Then the one just after half-time was the one we shouldn't have conceded.
“But he made some important saves and again in the penalty shoot-out.
“We hung in there trying not to concede that third goal and at 2-1 anything can happen in the last 20 minutes.”
Clough continued: “I thought the equaliser was coming after Lucas Akins' goal that was offside. It was no more than we deserved for hanging on in there.
“In the end I thought we could have won it late on through Calum Macdonald.
“We are trying to go toe to toe with these teams and you have to be patient at times as they are better than us. And the crowd have to be patient too and not get too frustrated as if we squeeze up to them they will cut us to ribbons.
“I thought Ollie Clarke really got us going and got the crowd up. We got more in their faces.
“Once we got to the last 20 minutes you really saw the crowd come into their own with the noise which was brilliant and despite Quarry Lane not being open I thought there was more than enough atmosphere.”
Clough was not surprised to see his side win again on penalties as they did in the last round.
“We have been good taking penalties in training and at Sheffield Wednesday so we saw no reason why we couldn't win the shoot-out,” he said.
“We don't coach them on them but we do say think about the height and direction and get some pace on the ball. You have to be clear what you're going to do as you walk up.”
He added: “It's early still so we just have to keep our feet on the ground, keep doing what we're doing, and quickly get our minds on Gillingham.”
On tomorrow's cup draw, he said: “Manchester United away is always an attractive ones for supporters and an opportunity to visit Old Trafford would be pretty special.”