Keeper Christy Pym made two saves to help Stags win a penalty shoot-out after a superb 1-1 draw away at Championship neighbours Sheffield Wednesday last week to reach round three for the first time since 2005.
Now they face Posh – the last pairing drawn out the hat – and Clough said: “I am delighted with it.
“I didn't see the draw as we were at the pub quiz and hadn't got any phone signal. But someone told me afterwards that there were six teams left in the hat – Leicester, Liverpool, Manchester City, Newcastle, us and Peterborough.
“So I would have taken Peterborough at home any day of the week, as tough as it's going to be.
“I know it's not as glamorous as Newcastle or Liverpool or someone like that, but we have an opportunity to get through.”
The tie will be played the week commencing Monday, 25th September.
Another one at the club delighted by the draw is former Peterborough United midfielder Louis Reed.
“It's always good to play against your old club and a chance to go through to the next round,” he said.
“Everyone is looking for the big ties but no one really wants to get run around by Manchester City. It is definitely one we can win and we will be looking to do that.”