Mata, Chelsea's player of the year for the past two seasons, has been linked with a move from Stamford Bridge after becoming a less central figure this term as he struggles to adapt to Mourinho's approach.
Mourinho has said the "door is open" but insists he wants Mata to stay, despite not being able to guarantee him a place in the team.
"I try to do my job, forgetting that I have a soft heart and pretending that I have a hard heart," Mourinho said.
"Many times decisions I have to make hurt me, but I think to do my job in the best way is to do it thinking that the team is more important than any player.
"When I have to make decisions I always try to be a cold one, icy, analyse the situation and try to make the best decision for the team and put the persons (involved) in the second level."
Mata has made 11 Premier League starts this term and reacted with frustration to his substitution in Wednesday's win at Southampton.
He could start again in Sunday's FA Cup third-round clash at Derby, where Mourinho has insisted he will select a strong team.
The former Valencia playmaker was part of the World Cup-winning squad in 2010 and in the year of Spain's title defence in Brazil can be concerned for his international position.
That is not a worry for Mourinho, who has Eden Hazard, Oscar, Willian, Andre Schurrle, Kevin De Bruyne and Mata competing for three positions behind a lone striker.
Mourinho added: "It hurts me, because the kid (Mata) is a good kid, the kid works hard and of course it's not an easy situation for him not to be playing every time.
"He's had lots of minutes on the pitch. And if he does it very, very well, I love it.
"If he does very, very well for us - for us, not for him, which is the most important thing - I'm more than happy with that. That's what I want."
Following the Southampton win, Mourinho intimated Chelsea would listen to offers for Mata if he wished to leave, but none have so far been forthcoming.
Asked what he would do if Mata asked for a move this month, a smiling Mourinho said: "I would say 'go to Stamford Bridge and speak with the board'. And I call the board to say 'don't let him go'."
Mata won the FA Cup in 2012 in his first season at Chelsea and will hope to play a part in a successful run this term in a competition Mourinho holds dear.
The Portuguese, who led Chelsea to the FA Cup in 2007, recalls watching FA Cup finals with his father as a child and speaking to his mentor Sir Bobby Robson about the magic of the tournament.
"As a kid in the time of black and white television, the English Cup final is one of the few matches we were waiting for," Mourinho said.
"That Coventry one (in 1987) I remember because I was with them. I was always with the underdog."
Mourinho disagreed with sentiments expressed by Aston Villa manager Paul Lambert that the FA Cup has become an unwelcome distraction for Premier League clubs.
"A trophy is a trophy," Mourinho said.
"Of course the League Cup is not comparable with the FA Cup, there is no comparison, but a trophy is a trophy.
"Everything matters. If you are a team without history in winning trophies, if you can do it - of course without forgetting the main objectives, which for many teams is to stay in the Premier League - I think people should try."