The capital club supremo argued that a spot-kick would have altered matters completely, but refused to complain too much even though his side have lost two in a row at home
The second defeat in the league at the Santiago Bernabeu this season does not come at an ideal time, with Madrid looking to overturn a two-goal deficit in the Champions League semi-finals against Barcelona on Tuesday night.
"The pace of the game increased gradually. We tried harder to score as the game went on. Some says nothing works and today was one of them. Zaragoza punished us with each counter-attack. They scored a lot of goals from few shots," he told the club's official website.
As has been a recurring theme with Real Madrid in recent weeks, Valdano felt that his side had been hard done by in terms of refereeing decisions.
He said, "There is no doubt that Kaka should have been awarded a penalty. It would have resulted in the game going to 2-2 and the match would have changed completely. The referee did not see it."
In spite of the setback, Valdano urged everyone at the club to remain confident as they attempt the improbable in the Nou Camp in midweek:
"Madridismo always believes in comebacks. If there is one team that has the habit of being heroic, it would be Real Madrid. Nothing should deprive us of feeling hope and excitement for Tuesday's match. We must have faith in our extraordinary players."