The result ended Wolves' poor recent run and moved them five points clear at the top of the table.
Sylvan Ebanks-Blake's second-half penalty was enough to see off the Eagles and secure only Wanderers' second win in 12 games in atrocious conditions at Selhurst Park.
"It's always about results," said McCarthy.
"When you've gone as long as us with only one win and then you come to Crystal Palace on a wet and windy Tuesday night, it's always about winning. And we could have won by more.
"I can't deny there's a sense of relief."
Wolves have only stayed at the summit thanks to the altitude sickness also afflicting Birmingham and Reading lately.
Ebanks-Blake missed a superb chance during Saturday's defeat by Plymouth Argyle, after which McCarthy branded his side "hopeless", but he calmly tucked his 74th-minute spot-kick past Julian Speroni for his 22nd goal of the season.
"He missed a penalty against Coventry recently and he was devastated after missing a great chance against Plymouth on Saturday," added McCarthy.
"But goalscorers have an inner belief - there was no doubt he was going to take it and no doubt in anyone's mind he was going to score it either."
Palace, themselves struggling for form and tumbling down the table, will count themselves unlucky with Paul Ifill rattling a post with a free-kick before Ebanks-Blake struck.
Eagles boss Neil Warnock was also fuming at the penalty decision, when Clint Hill was adjudged to have brought down winger Michael Kightly in the area.
"We're not having any luck, are we?" he said.
"The penalty is never a penalty. You can't blame him for cheating but the referee says he didn't give it, that it was a tangle.
"And if you look at the video, it is a tangle. There is no way a linesman 45 yards away can conclusively say that's a trip. I think it's scandalous.
"It's a cruel game sometimes, but that is what tests you."