McCarthy admitted his team has been second-best before the game turned on its head following Tom Lees' dismissal just after the half-hour mark.
David McGoldrick netted either side of the break, before Jay Emmanuel-Thomas completed the scoring to move Town four points clear of the drop zone.
"I'm pleased because it's the first time I can remember when we got away with an ordinary performance," McCarthy said.
"Leeds were better than us, certainly for 30 minutes.
"It was our turn to have a bit of good fortune and the red card changed the game.
"I don't think anyone could argue against it. It was a sending off, in my view.
"We worked hard. We were under the cosh and there was a time when we would have capitulated but it doesn't happen now.
"We make saves and blocks, stuck at it and kept a clean sheet until we had opportunities to score."
Of his side's ongoing battle to beat the drop, McCarthy added: "The whole league is bonkers and the pressure's starting to tell.
"You can worry like hell about other results, as I'm sure we all do, but you can only concentrate on your own results and performances."