Los Blancos overcame Segunda B side Alcoyano 4-1 on Wednesday evening and the Portuguese coach has claimed that they are treating the cup competition with respect.
"We are not in this competition to have a laugh," said Mourinho.
"We like the Copa and we certainly did not want to make the history books for the wrong reasons, as has happened to Madrid in the past in this competition. We did our job and so did Alcoyano.
"They were up for the game and played with enthusiasm and they have some interesting players and it seems they have a good coach because they played as well as I thought they would."
Mourinho's side will play Almeria in the last 16 of the competition.