Mourinho is widely expected to leave Madrid at the end of the season in favour of a return to Chelsea, and the home fans appear to have turned on their coach since the Blancos were eliminated at the semi-final stage of the Champions League to Borussia Dortmund last week.
The coach further divided fans' opinion with two fiery press conferences in the last week, in which he criticised club captain Iker Casillas and centre-back Pepe.
Mourinho's name was whistled when it was read out by the stadium announcer before the match with Malaga, but Karanka sought to play down the significance of the fans' ill-feeling towards his boss.
He said: "We don't pay much attention to that. In any case, the fans express their feelings while the coaching staff try to get the best performance out of the players. However, we respect their views."
Asked if Mourinho had given the half-time team talk, Karanka responded: "It was the same person that always gives it, the same guy that won the league last year."
Striker Gonzalo Higuain was also the victim of fan derision when he came on to replace Karim Benzema in the second half, but Karanka insisted the Argentinian still has the backing of the club.
"That's football. Last year the fans were shouting 'Pipa [Higuain's nick-name] please stay' after we won the league in Bilbao. We know he's not in the best form, but he has to keep on working. He knows what the coaching staff think of him."
Pepe was left out of the squad four days after saying that Mourinho had "shown a lack of respect" to Casillas in an interview after the 4-3 win over Valladolid, but Karanka insisted the defender had been excluded for footballing reasons, pointing to the form of 19-year-old centre-back Raphael Varane, who has been first-choice centre-back alongside Sergio Ramos since March.
"The squads are decided on each player's performances and everyone can see how good Varane has been," he said, before delivering a broadside to assembled journalists.
"Before you used to rip Pepe apart, now you are his defenders. It surprises me," he said.
The assistant coach gave no clues about where his future or that of Mourinho lay, but said that he would remain at Madrid if the Portuguese did.
"I'll decide when the moment arrives. If Mourinho continues, I'll stay with him, if he doesn't, we'll have to see. But there is still time to carry on working and enjoying myself here."
Cristiano Ronaldo hit his 200th goal for Madrid in the demolition of Manuel Pellegrini's side, but also had a penalty saved by Willy Caballero.
The former Manchester United player, who has been linked with a return to his old club, has not signed a new contract with Real Madrid yet, with his current deal set to expire in 2015, but Karanka said he believed the forward should stay at the Bernabeu.
"Madrid is the ideal place for Cristiano, and he is phenomenal for Madrid," he said.
Raul Albiol, Mesut Ozil, Karim Benzema, Luka Modric and Angel Di Maria also got on the scoresheet for the Blancos, while Roque Santa Cruz and Vitorino Antunes replied for the visitors, who had Sergio Sanchez and Martin Demichelis sent off.
Mesut Ozil had to leave the pitch before the end of the game with an apparent ankle injury, but Karanka was unable to give details about the seriousness of the injury.