Luton, 18th with 20 points, trailed Everton by one point with a game in hand before the reduction in the penalty for breaching the league's financial rules but the Toffees are now up to 15th on 25 points.
"We've been going off the league table with no deduction anyway, so makes no real difference. We were in the bottom three before, we are now," Edwards told reporters. "Situation is the same, really, from my point of view."
Nottingham Forest, who dropped to 17th place, are four points ahead of Luton, having played a game more. Forest, too, are facing a potential points deduction for breaking the league's spending rules.
Edwards said Luton would not depend on other teams having their points deducted to help them stay up.
"That can't be the thing that keeps us in the league. We've got to try and make it in our own hands... in a way it's good there's a bit of clarity," he said.
"It is important what other people do, but if we don't do our job it doesn't matter at all anyway."
Luton host holders Manchester City in an FA Cup fifth-round tie on Tuesday, before welcoming Aston Villa on Saturday in their next league game.
