Valdano was shown the door by Real president Florentino Perez yesterday after failing to work smoothly with the Special One.
Valdano said: "If the perception is that there was a fight between us two, Florentino Perez has made it clear who the winner of the fight was.
"I did not plan to resign. But now this has again happened. Real Madrid has taken the decision to create a new organization and the general direction without a sports director."
He added: "I do not know what was the intent of Mourinho. What I do know is that I have made every effort throughout the season to reduce the noise around him at Madrid. I asked the president for a meeting of us three to settle any differences, but it was not possible."