The visitors came away with all three points in snowy South Yorkshire with Joe Bennett netting the winner five minutes from time after he found himself unmarked from Josh Murphy's driven cross.

McCarthy said: "They're all hard-earned wins. Some just seem to be harder than others because of the nature of the game.

"Conditions weren't great and we had to fight fire with fire with free-kicks, throw-ins, corners.

"It was hard work. The squad has quality but we have had to show that fighting spirit.

"We had to play for seconds – it was that kind of a game and I thought the lads handled it really well."

It was a harsh defeat for Rotherham, who had dominated parts of the game and had fought back earlier in the second half with Matt Crooks tucking home an equaliser from close-range from Michael Smith's cross.

Cardiff had taken a first-half lead with Sheyi Ojo finishing one-on-one past goalkeeper Viktor Johansson after being freed in his own half by Harry Wilson.

McCarthy added: "I'm bitterly disappointed with the goal we conceded. But the two goals we got were very good ones.

"I'm really delighted with the performance.

"With the quality that we have in the squad, we should be sneaking up behind those in front of us rather than looking behind. I think they believe that.

"In this league you're not allowed to show that quality unless you win the scrap first.

"You have to make sure you're not getting beaten or caught on the break. You have to be purposeful and then you will get your chances."

Rotherham felt they had decent shouts for a number of penalties in the game with a shove on Smith looking the most likely.

Manager Paul Warne said: "We go through games of full luck or no luck. We rode our luck Saturday (victory at Preston) but I didn't think we had any tonight.

"I thought over the course of 95 minutes we didn't deserve to lose.

"I asked the lads to give everything they've got.

"It was just a misjudgement for their goal in the first half and their lad finished it confidently. We were well on top.

"I think we were more than deserving of a penalty for a foul on Smudge (Smith).

"We got ourselves back in the game and I thought we would go on and win it. All in all we come away disappointed but really proud of the way we played.

"The lads didn't do much wrong. Cardiff were quite happy to just play off Kieffer (Moore) and just have throw-ins and corners.

"There wasn't enough ball in play time. To come away with nothing seems a bit harsh."