Real have endured a difficult few days after they lost Wednesday's King's Cup quarter-final first leg 2-1 at home to arch rivals Barcelona and Mourinho's Portuguese compatriot Pepe was accused of deliberately stamping on Lionel Messi's hand.
Pepe said it was accidental but was widely condemned in local media, including the normally supportive Madrid-based sports papers.
Marca, the biggest-selling daily, reported on Sunday that Mourinho had rowed with Spain defender Sergio Ramos during Friday's training session and said there was a rift between Mourinho and some of the Spanish internationals in the squad.
At his post-match news conference, Mourinho batted away questions about the unsourced Marca report, twice interrupting journalists to insist that he did not read the paper.
Quizzed about Real fans whistling him during Sunday's game, the former Porto, Chelsea and Inter Milan coach said it was the first time it had happened to him in his career but that it was "not a problem."
"There is a first time for almost everything and it has happened to me. It doesn't matter," Mourinho said.
Home fans had also whistled former Real players like France's Zinedine Zidane and Ronaldo of Brazil, as well as current forward Cristiano Ronaldo, another Portuguese, he added.
"If they whistle me at a club where they don't whistle anyone, for example like Chelsea, it would be difficult to accept," he said.
"But at a stadium where they whistle the world's greatest, who am I not to be whistled at? It's no problem.
"Zidane responded with his football, as Ronaldo did, Cristiano continues to do so.
"I will continue working and maybe one day I can respond and maybe one day they will be sad."
FOOTBALL PROFESSIONAL
Real President Florentino Perez hired Mourinho from Inter at the end of the 2009/10 season to try to end Barca's Spanish and European dominance and the Portuguese said he had an excellent relationship with the club's board of directors.
"I am a football professional who tries to defend the colours of Real Madrid with dignity and to the best of my ability," he said.
"I haven't asked anyone for the right to coach Real Madrid, it was Real Madrid that asked me to coach them. I am calm and I do my work and do the best I can."
Emilio Butragueno, a former Real striker who is now director of institutional relations, said the club would not have been able to open a five-point lead over Barca in La Liga and win all six of their Champions League group games if there were problems in the dressing room.
"It would be impossible to put together this campaign if there was any fracture," he told Spanish television.
"If you look at the La Liga table, there is no doubt about the unity," he added.
