Arsenal won through two own goals, with the second - on 94 minutes - coming after Tolu Arokodare had struck Wolves' equaliser in the 90th minute.
Edwards declared afterwards: "The lads gave everything tonight. We're flat, because the bottom line is we lost another game of football. That's why Arsenal are where they are, they found a way and we also found a way to help them, I think. I can make all the excuse in the world, I can say it's Arsenal away and all of that, but we've lost the game.
“The lads gave everything. I'm proud of a lot of it tonight, but it hurts. I hate losing games. We all do. We've lost far too many, but I think we're going about it in the right way to try and turn things around. You can see it tonight – there's a team that's committed. They're sticking together, they're fighting, and I feel for the supporters.
"A big thank you to them for coming all the way down here and backing us right to the end there. I feel for them, because it'll be hard for them at the moment.”
On his game plan, Edwards continued: “The plan did work. The lads carried it out really well. We were very disciplined. We obviously can't open up here, we’d be asking for trouble. So, we were a lot more compact than we were on Monday – different game, different opposition, and it was the right way to go.
“The lads worked hard on it. They believed in it, and we had to wait for our moments to show the courage to get back in it after going 1-0 down. We started pushing, we pressed, we made changes, got back into it, but this is why we are where we are. We've got to value stopping the cross. We’ve got to defend the goal, and we're not doing that well enough.
“They limited Arsenal to quite little, for them. The two goals we conceded are quite bizarre, especially the first one, but to get back in it, to work that hard and show a lot of fight, a lot of spirit, a lot of courage, all the things that we were asking for, things that aren't in our control, then to lose it very late on hurts.”