Wrexham were 2-0 up at halftime and while Forest fought back to have the scores level at 3-3 after extra-time, they were knocked out of the Cup after losing the penalty shootout.
Present was Reynolds and Parkinson said afterwards: "He totally gets it.
"I had a chat with him before the game, and it was great to see him over here with his family. I think Ryan’s mum was here tonight, which was for the first time. So it’s really special, and I hope they’ve enjoyed the night.
"I’m sure that on the flight back home tonight, they’ll be having a few glasses of wine to celebrate."
On the tie, Parkinson also said: "We had to rally the troops a bit in the break, because I think the whole ground had gone flat.
"You get that feeling, ‘have we lost our best chance to get through and beat a Premier League team’? But the lads rallied themselves, there were a lot of tired legs, and credit to both sides for putting on such a good game after that busy Christmas schedule."
He added, "It’s a huge night for us, and I’m pleased for this group of players to write their own bit of history in the club’s rich heritage in the FA Cup."