The 20-year-old midfielder was handed his marching orders by referee Martin Atkinson after just 23 minutes following a challenge of Luis Suarez.
The club have since confirmed that they have lodged an appeal against the decision to the Football Association and Neville hopes that it will prove to be successful.
"Hopefully sense will prevail and the red card will be rescinded," the 34-year-old told the club's official website.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.
"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."
Everton lost the match 2-0 to neighbours Liverpool.