Williamson was dismissed for a challenge on Southport striker Mark Duffy in injury-time, but after seeing a recording of the incident, manager Dean Saunders â€œ who described the refereeing as farcical â€œ believes there are grounds for appeal.
"It was never a red card and we are going to appeal against it," said Saunders today. "Sam was harshly done by, it was a foul and a yellow card at worst.
"There were two other challenges that were worse in the middle of the pitch.
"The game got ruined for the spectators, the players â€œ everybody."
Wrexham had already been reduced to ten men when Steve Evans was red carded for a foul from behind on substitute Steve Daly who converted the penalty to cancel out Marc Williams' opener for the Reds. But Saunders will not appeal against Evans' dismissal.
"Steve's sending off was a bit dodgy as well after looking at it yesterday morning," said Saunders. "But I can understand that one, I can't understand Sam's."
Pleased with how his side performed for the first hour, Saunders said the defensive error leading up to the equaliser and the handling of the game by the referee changed the shape of the game.
"I was really pleased with how we played for an hour, pleased with some of the football we played and the attitude of the players when we started the game off," said Saunders.
"We were patient and eventually Marc scored a good goal from a great ball by Nathan Woolfe.
"Everything was going to plan and then, a quarter of an hour into the second half, the whole game turned on its head.
"It was suicide defending, and then the game got ruined."
Several players who have not featured in recent weeks were given their chance by Saunders who was delighted with a number of impressive performances.
He praised substitute Andy Fleming â€œ back after nearly two months on the sidelines â€œ for his display, but he had also been hoping to give another long term absentee, Kyle Critchell, a run-out.
"I made five changes as I needed to see them play," said Saunders. "I needed to know what I was going to do if I got injuries.
"I learnt a bit, and I thought Christian Brown was excellent. Marc, Sam and Jon Brown were outstanding, and Andy when he came on did really well.
"I was hoping I could bring Kyle on and give him a game, and bring Andy on for the last half hour, and Patrick Suffo on for Marc â€œ I had it all planned out in my head. I was disappointed I couldn't get Kyle on."
Wrexham take on Mansfield Town in the FA Trophy first round tie at The Racecourse tomorrow, and although Saunders is hoping to progress to the last 32 of the competition, he knows the importance of challenging for promotion.
"Nobody is safe when you lose to Southport," added Saunders. "I have got a team in my head for Saturday.
"Cup games are important, you have got to try and win every game you play.
"It is also vitally important we get out of this league so all my thought processes are gearing towards that.
"I didn't sleep because we got beat on Tuesday. But football is full of punches on the chin, you have to get up and walk through them or curl up in a ball and stay in bed."