Referee Anthony Taylor chose not to show Ridgewell a card for the tackle but the FA this week dismissed reports that retrospective action would be taken against the Birmingham defender.
Martinez maintains that Taylor should have sent Ridgewell off, but McCarthy escaped without any lasting damage and the Latics boss accepts a suspension for the defender now would not aid his team in any way.
"What you need is the punishment for the action to be handed out in the game," Martinez told the Wigan Evening Post.
"At that moment, we were well on top and it would have been a big, big decision in the game that would have helped us get the rewards we deserved.
"It would have been ridiculous to look back at it now and punish the team by taking out one of their best players for a game against another team who could be fighting for the same aim that we are.
"That would make Birmingham weaker for a game against a team who might be one of our rivals, and the whole thing would make no sense to me at all.
"If officials don't see something during a game, that should be it. There should be no action afterwards."
Martinez believes various incidents over the last few weeks demonstrate that the standard of refereeing needs to improve.
"What they have to do - and I have said it time after time after time - is they have to be better at getting the big decisions right," Martinez said.
"If you look back at the last three matches, you could put a good DVD together of huge mistakes made in big games.
"Look at the Aston Villa game against Manchester United, our game against Tottenham, and again at Birmingham last Saturday.
"There are just too many big decisions being made that are wrong that are clear for everyone else to see."
Liverpool 8/13, Draw 5/2, Wigan 5/1