Nathan Jones presided over much of the recovery during two spells as manager, winning back-to-back promotions in 2018 and 2019.
And the momentum was maintained after Jones left for Southampton last November.
Edwards, who took over soon after being sacked by Luton’s arch rivals Watford, has won 16 and lost just five of his 31 matches at the helm.
“We’re one game away from the Premier League. It sounds special, it sounds surreal saying it,” Edwards added.
“We are, it’s a fact. And I’m really, really happy.
“The fans were great, and we needed them. They got the atmosphere going before kick-off. When the staff came in after the warm-up they said the atmosphere was really, really good.
“We were just glad we were able to repay them with a good performance.
“If we didn’t believe after being 2-1 down and being right in the game, then what’s the point?
“We believed from day one that we could achieve something. We’ve got one more game to go to try to do it, I’m not getting carried away.
“I’m really proud and want everyone to enjoy the moment of winning a semi-final.
“We’re going to go to Wembley for a day out and it’ll be really special.”