The Portuguese coach says his side are taking the cup seriously, despite making nine changes from the team that beat Mallorca 5-0 in Los Blancos' previous outing
Karim Benzema scored twice in Valencia, while Kaka and Jose Rodriguez were also on the score-sheet for a Madrid team whose only survivors from Sunday's Liga victory over Mallorca were Michael Essien and Raphael Varane.
"We are not in this competition to have a laugh," the Portuguese coach told reporters.
"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."
The 49-year-old also responded to recent criticism in the Spanish press for allegedly not using enough academy graduates.
"I look for a balance between the first team and the academy," said the former Chelsea and Porto boss.
"Nacho is an option at left-back, but he will never play centre-back. He has a bright future as a left-back."
Mourinho added that he wanted players "who will play for Real Madrid for the rest of their lives".
Meanwhile, young midfielder Rodriguez was delighted at marking his Madrid debut with a goal, at the tender age of 17.
"The dream of all youth players is to play in the first team," said the former Spain Under-17 international.
"My parents have recorded the game. The truth is, I didn't expect it, and I'm very happy. It made me very excited that Mourinho called me.
"It was a good goal but the most important thing was the team winning."