Stags won the shoot-out 5-4 after Rhys Oates' late goal had earned a 1-1 draw over 90 minutes and are in the third round hat for the first time since 2005.
“We were so unlucky not to get a result here last year in the FA Cup so this goes some way to make up for it,” smiled Clough.
“I thought second half we were absolutely outstanding – it was just whether we could get the goal or not. What a goal it was in the end – I just counted 32 passes leading up to it and a magnificent burst of pace and finish.
“This result is not a fluke or a one-off. We have played like in most of our six games which is why we are unbeaten.”
He continued: “Their goal was a bit soft in the end. I think Lewis Brunt got pulled out of position, but it was a good cross, a great head back and it was a simple finish from there.
“I don't think we took advantage of the positions we got into in the first half. But we were up against better players and better defenders.
“We just needed that one piece of brilliance that we got in the second half. On that second half performance it was deserved. We seemed to grow in confidence as the game went on.”
Pym saved two of the Wednesday spot kicks and Clough said: “Once it went to penalties it was a lottery and Pymy has come up with the saves.
“I think with them getting through on penalties in the first round, to win two on the spin doesn't happen too often so from that point of view I thought we were due a break.
“I thought Christy played very well. You have to when you come to a Championship club who have put almost a full side out. Your goalkeeper and defenders are going to have to play well and I thought Christy made some crucial saves.
“We said to them at half-time just stay in it at 1-0 – then anything can happen like Newcastle v Liverpool at the weekend. Concede a second and the game is over.
“I would like a home tie but I don't really mind who we play.”