Luton earned their first point of the campaign against 10-man Wolves after Carlton Morris cancelled out Pedro Neto's opener in a 1-1 draw. It was their first point in the top flight in more than 30 years.
"Everyone can stop talking about Luton being the only team not to have anything. We've got that off our backs," Edwards told BBC Sport after the bottom side became the last team to get on the scoreboard in the league standings.
"It shows at this level how hard you have to work, almost perfect to get something from the game.
"I'm really proud of everyone connected to the club. We showed what we're about, The performance was brilliant."
Backed by loud home support at Kenilworth Road, Luton looked far from the side that struggled for points in their first four games while a far more experienced Wolves side were clearly rattled, especially after Jean-Ricner Bellegarde was sent off in the 39th minute.
"We were the better team throughout, we completely dominated. Wolves have quality players who can hurt you. We showed character to come back into the game," Edwards added.
"We were on the front foot, we were aggressive. We were fast... We just couldn't find that little bit of quality.
"But it's coming. We were better again today. I'm not saying we should have got something from the game, I'm saying we should have won."
