The result leaves Luton three points from safety.
Edwards said: "It's this club, Luton Town, we've got to fight, we've had to do that for a long time. I've come in over the last 18 months and learnt that.
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"There is no other option than to keep going and keep fighting. The players have shown quality and bravery as well as that fighting spirit.
"We'll never give up, we'll always keep going. They're a special, special group.
"To be 3-0 up and lose the game midweek was tough for us all, so to come back in such a big game - and for Luke Berry, who has now scored in every league, to get that equaliser is a really special moment for him and this football club."