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 in Istanbul ahead of Wednesday's Champions League game at Galatasaray, instead attacking the individual who leaked a private conversation.
Asked by Sky Sports News' Bryan Swanson whether he was embarrassed his comments had been made public, Mourinho 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."
Watch Chelsea take on Galatasaray live on Sky Sports on Wednesday. Coverage begins on Sky Sports 1 at 7pm
Mourinho has consistently played down his side's chances of winning trophies this term but still believes his Chelsea side can go all the way to Lisbon.
He said: "We are not favourites - that's obvious - but I think when a team reaches the quarter-final anything is possible, so I think this round is very important for every team.
"The ones that reach the quarter-finals can start having a little feeling even if they're not a favourite: Chelsea won (in 2012) when not favourite, I won it twice when not a favourite, and I didn't win it when my team was one of the favourites to win it.
"This competition, because of the knockout format, has a little space for a surprise but it's clear there are at least three, maybe four or five teams that are by quality, experience and status obviously favourites."
Galatasaray may lack the Champions League pedigree of Barcelona, Real Madrid and Bayern Munich, but they beat Mourinho's Madrid in the home leg of last season's quarter-finals.
Roberto Mancini has since replaced Fatih Terim as boss, but the likes of Didier Drogba, Wesley Sneijder and Felipe Melo remain at the heart of the team.
Mourinho said: "They were a good team then and they are a good team now. "If last season was very difficult for Real Madrid this season for Chelsea is not going to be different."