The Goodison Park club were docked 10 points for breaches of the Premier League's profitability and sustainability rules (PSR) in November, but that punishment has been changed to six points on appeal.
Everton face another possible points deduction after being charged in January with breaching rules for a second time, relating to the three-year assessment period running up until the end of last season.
Nottingham Forest, now one place above the drop zone, have also admitted to breaches of financial rules.
Third bottom Luton are four points from safety, with Everton leapfrogging Forest and Brentford up to 15th as a result of the appeal.
Speaking ahead of Tuesday's FA Cup fifth-round clash against Manchester City, Edwards, whose side are in their first season back in the English top-flight since 1991/92, said he welcomed the "clarity".
"It was going to be hard anyway," he said. "We're in a difficult league and it's been tough from day one. There are more (potential) charges, but that's completely out of our hands and control.
"What's in our control is our performances, how hard we work and I wish we can control results, but we can't. If we don't do our job then it doesn't matter anyway."
Edwards, whose team have suffered three straight league defeats, said: "It's something none of us have really experienced before.
"But it's out of our control and all we really care about is Luton and that we need to get enough points to stay in the league.
"I don't want to rely on other things and external factors which we cannot control."
