The Hatters were 3-2 up against Arsenal at home, but were pegged back to 3-3 with time left in the game.
Edwards admitted he was left almost speechless, telling reporters: “I didn't really know what to say to the lads afterwards. What I did say was I'm proud of them, not to let that one moment then affect us too much.
"I've got to look at the bigger picture, they did exactly what we asked of them, gave everything, and football is about entertainment. It was an entertaining game, but my job is to get points as well and we've just come up short today.
“I don't think I've ever seen them so disappointed and flat, they were hurt by it, we all were, but all I can say to them was they gave everything, they made the supporters proud.
"The fans were all standing at the end and standing up and clapping, so we know we doing our job when they're doing that. The difference tonight between a 3-3 and a 4-3 was just those few seconds, so we can learn from it, but if I can almost eliminate it from how I feel about the game, then really, really proud of the players.
“Every game's different, our performances have been good and you're playing against a top team like that you know you have to up it and know you have to give even more as they're going to test us even more, ask more questions and they did that.
"I think we made it a really uncomfortable night for them, they want a game of order and control and we tried to make it chaotic, we tried to be really aggressive and brave and then we showed some really good quality as well on the ball in the moments that we had it.
"So I think we can take some positives from it and we have to, but we know we need to get points as well, performances are things that will get us those."