Wolves won 2-0 thanks to second-half goals from Joao Gomes and Rodrigo Gomes.
On his emotions, Edwards declared afterwards: "Elation, relief! I know how big a game this is for us and our supporters. It's a Midlands derby and we take pride in it. When the final goal went in, it was the final nail in the coffin and I could enjoy the final 20 seconds.
"Villa are such a good team with loads of individual talent and quality, so you have to do your job. In transitional moments we needed to be clean, go for it or stay behind.
"In defence there was a great desire to keep the ball out of the net."
On winning the derby despite their position in the table, he continued: "It's special, really special. It's been hanging over our heads. It's not something I've focused on. To do it in this game, with everyone watching, it was important, it keeps us moving in the right direction.
And on his touchline celebration for the second goal, Edwards laughed: "The old calf was close to going, I'm not at top speed. I was conscious of not falling over! My family was over in that corner, so it was nice to have that moment with them. I lost myself a bit there."