Mourinho was caught on camera at a commercial event as he told a businessman: "I have a team but no striker".
The Chelsea manager also joked about Cameroon international Samuel Eto'o's age, saying: "I have Eto'o but he is 32, maybe even 35."
Mourinho did not attempt to defend his comments as he faced the press ahead of Wednesday's Champions League game at Galatasaray, instead attacking the individual who leaked a private conversation.
Asked whether he was embarrassed his comments had been made public, he said: "You should be embarrassed as media professionals.
"From an ethical point of view, I don't think you're happy - not you (personally) - that a colleague is able to record a private conversation and make it public. From an ethical point of view, it's a real disgrace.
"I'm not defending what I'm saying. I'm attacking something fundamental in your professional area. That person showed exactly what he doesn't know about the job.
"From my perspective, the (Eto'o) comment is obviously not a good one, and not one I would do in a serous way or an official way: first of all because I don't make fun; secondly because if there are managers in the world that really defend players I'm obviously one of them; third, because Samuel Eto'o is Samuel Eto'o.
"He's four times a Champions League winner - people think three, but four. I was with him at Inter when I had the best ever season of my career, and he's one of few players working with me in a second different club: a manager never does that when he doesn't like the player or person.
"He has no reason to be upset. Also he said a few years ago 'Mourinho is the only manager I would never play for'. After one year he was with me at Inter, and now he's here. There is no story."
Mourinho was less forthcoming when asked if he had spoken to his other strikers, Fernando Torres and Demba Ba about the leaked conversation.
He said: "If you are ready to speak about the game now, I'm ready."