To ensure they drive home their advantage, the Welsh have quickly turned their attention to Saturday's (NZT) match against Fiji at the Millennium Stadium, Edwards said.
"We didn't come into this competition, after the bitterness of 2011 [semifinal exit], to just beat England. We want to go as far as we can that's still uppermost in our minds.
"There's a word in sport which you need to be a great player or a great team and that's resilience because not everything's going to go your way. It's the same in life.
"Sometimes you just have to dig deep and show the resilience and I think that's what our guys did yesterday and good on them."
Gatland appeared emotional in the aftermath of the victory and Edwards remained so today. Often an intense and brooding character at press conferences, the former England league international spoke eloquently at his team's base on the outskirts of Cardiff about what the result meant for him and Gatland, who he said was a key part in getting the Red Dragons to believe in themselves.
"Warren said it was up there with some of the best games he's ever had in his life and that's including the third test with the Lions [against Australia in 2013]. I think it was the adversity the team came through. Even going into the game people knew we had some world-class players missing. We lost players going along, we were behind twice by 10 points ... so all that mixed in makes the victory even more special.
"You always look to your leader, to your boss, for your guidance and he certainly showed that. His pre-game speech was very calm but also had emotion in it. He mentioned that rugby is a very emotional game and you have to bring that emotion to the table when you go into big games."
- By Patrick McKendry in Cardiff