Referee Martin Atkinson has come under heavy criticism for dismissing the 20-year-old just 23 minutes into Saturday's 2-0 win for Liverpool for a tackle which most observers did not even think was a foul.
Everton have appealed against the sending-off and Neville is hopeful Atkinson will admit his error and wipe the slate clean for the young midfielder.
"Hopefully sense will prevail and the red card will be rescinded," he told the club's website.
"I don't think it was a sending-off, it was a bad decision but we all have bad days - we all play badly, but we don't think we got the rub of the green with decisions.
"It was just a poor decision. I don't want to have a go at referees because they have an unbelievably tough job and he doesn't need me telling him that he was poor but it's a bitter pill to swallow because we lost the game in the manner that we did."
Goalkeeper Tim Howard, who saved a Dirk Kuyt penalty late in the first half but could not keep out goals from Andy Carroll and Luis Suarez, felt Atkinson failed to get to grips with the whole occasion of one of the world's oldest derbies.
"It was the furthest thing from a sending-off you could see," the United States international added on evertonTV.
"I don't know about his positioning and whether he could see properly or not but it was the wrong call, particularly in a derby.
"You need to be strong and calm the emotional atmosphere.
"All that did with the wrong call was electrify both sides even more and it is not what that game needs.
"All in all it had a huge negative effect on the game."