West Midlands official Andre Marriner initially booked the wrong player, Christophe Berra.
But he finally realised it was Ward who should have received a second yellow card, and then a red, for a foul on Lucas Leiva just minutes after he had been cautioned for pulling Yossi Benayoun's shirt.
McCarthy sarcastically applauded his opposite number as the officials finally arrived at the right decision to dismiss Ward.
McCarthy said: "The referee did get the right player, but he had some flipping help, didn't he?
"I just wonder if he had any assistance. I did not think that Phil Dowd (the fourth official) knew who it was either, but people were in his ear about it.
"I don't know if Phil Dowd told the referee who it was. I wonder that if you can get assistance from the fourth official, maybe Ireland would still be in the World Cup.
"Without that (decision), we would have got something from the game. We had enough chances.
"But we gave a good account of ourselves and they needed a break. And they got it and took advantage of it."
He added: "I believe the referee was told who it was (who should have been booked). He wasn't sure and was told fairly quickly.
"Of course, it is good for the game, definitely. I can't see why they shouldn't help out, but you just bitch about it when it happens to you.
"They should get the right decision, be it from TV or the fourth official. I would have wanted the same if it had been me.
"It was very frustrating, disappointing. We had played well for an hour and looked comfortable enough.
"I was not convinced by the sending off and how much contact there was with Stephen Ward and Lucas. I cannot see it.
"I was annoyed with Rafa (Benitez), fed up, I wanted to win. We had an exchange. I applauded because I felt he helped get the lad sent off.
"I'd have probably done the same. We are not out there to be the best of mates, I'm OK with him now, it's the way it is."