The Wolves boss has no doubt opposite number Neil Warnock will use the problems facing the club as a motivating factor, with the prize of a home fifth-round tie against Aston Villa at stake tomorrow night.
"Neil will be all right," said McCarthy. "Talk about resilience and toughness, I think he has shown all of that.
"It is a difficult position for him. But Neil is the master of getting the best out of his team. He is one of the good ones. He will relish and will use it to motivate his team.
"He will use this 'all the world's against them' to get them fighting against us and knowing that the prize is a game against Aston Villa, which would mean money in the coffers. So it would help their cause if they were to win.
"They will be like a wounded animal, without any doubt. They had a good win at the weekend [2-0 against Peterborough] when their problems didn't seem to bother them.
"Being seen as the underdog and having a lot of problems just makes you fight harder."
Wolves needed Ronald Zubar's 84th-minute volley to spare their blushes in the first game at Molineux as they twice came from behind to snatch a 2-2 draw.
The lure of facing Champions League-chasing Villa in the next round is a juicy carrot for both clubs, and McCarthy is keen that his side's spirited fightback should not have been in vain.
"For us to have Villa at our place in an FA Cup tie would be fabulous and everyone would be looking forward to it," he continued. "But Palace are at home and they will fancy upsetting the odds. Selhurst Park is a difficult place to go and play.
"We have to make sure that we really do concentrate on this game first before thinking about Villa because it is going to be a really difficult game to get through. Let's not look beyond this game.
"But we want to stay in the cup, otherwise there would have been no point putting in all that effort to get back into the first game.
"I would love to win this game, beat Villa and then tell Manchester United that we could not play them when we are scheduled to in the Premier League because we are in the FA Cup, that would be fantastic. That would be sweet because it is normally the other way round with Manchester United."
Wolves head into the game on the back of battling draws against Liverpool and Hull in the Premier League, and McCarthy added: "We are playing well and we are fighting and scrapping for each other which is what we need."