Trailing 2-0 in the first half to goals from Demba Ba and Jonas Gutierrez, Halsey first failed to spot a clear foul by Steven Taylor on Jamie O'Hara inside the area.
Instead, Halsey awarded a free-kick just outside, denying Wolves a penalty and a chance of at least going into the dressing room at the interval in with a fighting chance of salvaging something.
Then in the first minute of five added on at the end, and minutes after a diving header from Steven Fletcher had set up a grandstand finish, there came another crucial decision.
Halsey relied on one of his assistants to make the call on a left-wing cross from Adam Hammill that was nodded back by Matt Jarvis and turned home by Kevin Doyle.
McCarthy was adamant that the ball had not crossed the dead-ball line and that his side were robbed of a share of the spoils.
"I guess you'd like me to blame them (the officials), and I'd probably be justified in doing so," said McCarthy.
"But we gave two goals away to start with which came right out of the blue.
"We didn't defend a corner particularly well, and then conceded another soft one, albeit it was a good finish. Before that we had enough chances to be in the game.
"But when you're having a tough time you do rely on people getting decisions right, and quite clearly they got them wrong.
"Mark Halsey said he didn't want to guess, well I guess he did because he got it wrong. He guessed wrong. He (O'Hara) is a good yard inside the 18-yard box, not just a little bit.
"And when you've worked as hard as my lads have at the end of the game to get the equaliser, to have another decision go against you tends to rip the heart out of you a little bit."
McCarthy found an ally in Newcastle boss Alan Pardew, whose side are now unbeaten in their last 10 league games stretching back to the end of last season.
Asked if his side deserved the win, Pardew replied: "I don't think deserved is the word I'd use today.
"We did play well in the first half which gave us a platform to win the game, but Wolves were very good.
"I watched their last two performances here when they were beaten, but they were a lot better today, and they can take great heart from it.
"In my view, if you want to use the word deserved, they deserved something from the game themselves.
"We were a little fortunate with that decision at the end. I've seen it. It's really tight."
As for the penalty, again Pardew backed McCarthy, adding: "I saw the fans' reaction and I honestly thought it was a penalty. I had already accepted that one.
"To be honest, I don't think that could have been the worst thing to happen to us because at half-time when you're 2-0 up the psychology of the dressing room is different.
"I think we felt we were comfortable, but you are never comfortable here, as has been proven over the years.
"We've not won here since 1990, so it's never an easy place to win."
Pardew's words were but a crumb of comfort for an appreciably unhappy McCarthy, who added: "Pards is honest enough.
"Why would he say anything else when he knows different? It would make him look silly, and he's not that.
"He's an intelligent bloke. He's honest about it, and they've got away with that one today."
In the end Newcastle were also indebted to goalkeeper Tim Krul for five excellent saves, resulting in rightful praise from Pardew.
"He's had more work to do today than in three of our games. That's why you need a good goalkeeper," said Pardew.