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McCarthy said: "Damien Duff plays a physically demanding game and excels in one-against-one situations. He was outstanding against the Danes tonight.
"Niall Quinn, sitting beside me in the dug-out, turned to me after just three minutes and said that Damien had already won the man-of-the-match award. How right he was."
Crystal Palace striker Clinton Morrison capped an impressive full debut with a superb second-half strike, after Leeds duo Harte and Robbie Keane had put the home side into a commanding lead.
McCarthy was pleased with his side's performance and felt the scoreline flattered Denmark.
"This was a difficult looking game for us on paper," he said. "But at the end it wasn't difficult, and we might have scored even more than three goals.
"Now I have loads of options as Robbie Keane and Clinton Morrison did very well up front. It would have been a psychological boost for Robbie to score against the Danes, just as he did at Lansdowne Road against Russia last month.
"I was particularly delighted that Clinton scored the goal he deserved in added time, as he had performed exceptionally well throughout the game and had a good understanding with Robbie."
McCarthy also revealed that he has yet to decide over who will make up his 23-man World Cup squad, but says he has a good idea as to who will board the plane for Japan and South Korea.
"I won't name my 23-man squad to travel to Japan this summer - certainly not until next month's game in Dublin against the USA. Put it this way, things are progressing nicely," added McCarthy.