Josh Windass struck the winner in the final seconds of extra time to send Wednesday up to the Championship. Father Dean had scored himself at Wembley in a Premier League promotion playoff victory for Hull City.
"It's the stuff dreams are made of," Moore said.
"You couldn't write it. It finished a titanic game that ebbed and flowed both ways.
"This is a special moment for me because it means so many people in Sheffield are happy and positive. When a football club does well you see the knock-on it has in the city, in the community.
"It goes to show that the impossible can be achieved. It's a fairytale story."
"For Liam and Barry, they have seen some good moments here and some which they will wish to forget," 49-year-old Moore said.
"They have been absolute stalwarts for the football club and to be part of a successful team, they will know what it means.
"It goes to show what can be achieved when a club comes together. It's been a long journey but a worthwhile one."