Dunne shot a nine-under-par 61 on the final day of the tournament to finish three strokes ahead of his closest rival for his maiden European Tour title.
McIlroy carded a round of 63 on Sunday - his lowest score of an injury-plagued season - but it was not enough to give him a first victory in 13 months.
Speaking to reporters, the Northern Irishman said: "It was nice to have a chance to win a tournament. The more chances I have like that the better. It's unbelievable [for Dunne] to shoot 61 to win his first tournament, it's very well deserved."
McIlroy will bring his disappointing season to an early end at the Alfred Dunhill Links Championship next week.