"They have the Premier League, they have the French league, they have the German league, they have the Portuguese league, they have the Dutch league.
Speaking to reporters before his side face Anderlecht in the Europa League play-offs, he said: "I show I am a special one, not the special one.
The Argentine had labelled Mourinho as "the crying one" as a reference to his "special one" nickname coined all those years ago when he first joined Chelsea.
The Fenerbahce boss saw his side fight back to earn a point as United tossed away the lead for a third successive drawn Europa League match.
Icardi had then replied by posting a meme of the "crying one" on his Instagram story, thus prompting Mourinho's next response.