The Hatters lost 2-1, despite taking the lead as Edwards pushed is players to not sit back against the champions.
Edwards later said, “Proud of them but I am disappointed as well today. I felt like it was there for us today, I had a really good feeling going into the game.
"Complete respect for Manchester City and what they are and who they are, credit to them for winning the game, but I just felt it, and the time of the goal just before half time, felt this could be our day. We're disappointed with the goals we conceded, but we look at that and we've got to keep working on that and improving.
"I thought we were so brave, without the ball being as aggressive as we were against a top team like that. There were a lot of problems for them to solve, which they're capable of doing, but then with the ball again, really brave and showed a lot of quality as well.
“The goal was a really good example of that, we tried to take the ball when we could, as we knew we couldn't just give the ball back to Manchester City otherwise you die a slow death. Everything about my team today, I really, really liked."
On the absence of Erling Haaland, Edwards added: “I think he's clearly one of the best strikers in the world isn't he, so it probably makes them a little bit of a different team, a different challenge. But again, world class players that are coming on his place, so they were still pretty good weren't they?"