The Spaniard dismissed the significance of the Portuguese's remarks, after the coach revealed he wished he had signed Diego Lopez sooner
Goals from Angel Di Maria, Kaka and a Cristiano Ronaldo double saw off the visitors in a gripping encounter but, though the Blancos boss was jeered and Iker Casillas cheered in the pre-match line-up announcement, Karanka moved to quell any controversy.
"You have to respect the jeers for the coach, as I said after what happened in Dortmund. For the last three years, we have done our work, which people can like more or less. I respect them," he told reporters after the victory.
"The reason we didn't come out into the technical zone is because we believed there wasn't anything worth saying. What there was to say, we discussed in the dressing room."
The win was overshadowed by Pepe's claims Casillas had been disrespected, however, after Mourinho said on Friday that he wished January signing Diego Lopez had arrived earlier.
"I haven't heard what Pepe said but, if he said that there has been a lack of respect towards Iker, at no moment have we disrespected anyone," the 39-year-old continued.
"It would be a lack of respect to 25 team-mates if you selected someone who was not in a condition to play. The lack of respect would have been to select a player who wasn't right, instead of another.
"It is not that Mourinho regrets it [not signing Diego Lopez after his first year], but his signing was requested and the club did not accept it.
"It is said that the coach has so much power, but it can't be so if a player is requested and the club don't bring him in."
Madrid's victory over Valladolid means Barcelona will not be able to lift the Liga title on Sunday, even if they beat Betis.