Wolves pushed the Gunners all the way and thought they had snatched an equaliser with Tolu Arokodare's 90th minute header.
But a Yerson Mosquera own goal four minutes later - which came after Sam Johnstone's own goal initially gave Arsenal the lead - broke Wolves hearts and Edwards said the players were devastated.
He said: "It was bad luck, but they earned it. That's why they are where they are, they're a brilliant team.
"I'm not going to complain about luck. I'm proud of the lads tonight, but obviously it hurts that we lost the game.
"It's tough when you're losing games, but performances can help.
"We saw a really committed performance. We're struggling at the moment for results, but we're not searching all the time for performances.