Tottenham midfielder Eric Dier entered the stands and confronted a supporter following the team's FA Cup fifth-round defeat to Norwich City amid a row involving the player's brother.
Spurs exited the competition in a penalty shoot-out on Wednesday, as Tim Krul saved two spot-kicks following a 1-1 draw after extra-time.
Dier scored his penalty but appeared irked by the actions of a fan following full-time and marched into the stands.
With the stadium emptying, stewards separated the England international from the individual involved, with clips of the clash quickly emerging on social media.
Asked about the altercation in his post-match media conference, Mourinho said: "I don't think that belongs to the game. The game was a fantastic representation of the FA Cup, but I cannot run away from the question.
"I think Eric Dier did what we as professionals cannot do but when someone insults you and your family is involved, especially your young brother...
"This person insulted Eric, the younger brother was not happy with the situation, and Eric was not happy. We as professionals cannot do what he did."
Mourinho did not want Tottenham to punish Dier for his actions, adding: "If the club disciplines Eric Dier, I would not agree with it. But what he did was wrong."
