Mourinho hit out at Spanish authorities last week after his side drew 0-0 against Deportivo on Saturday – just days after their 1-1 draw with Lyon in the Champions League.
The coach felt the game should have been played on the Sunday allowing for “an extra day of rest”.
Di Stefano agrees with the coach, and said he is always fighting hard for the best of his side.
“What Mourinho says always makes the headlines… he is defending Real Madrid, and we should be supporting them,” Di Stefano told Marca.com.
“As for the calendar, I think some of the late kick-offs are excessive for those fans who have to go to work or for young people studying.”
Meanwhile, Di Stefano hailed injured Cristiano Ronaldo, who could miss the Lyon return next week.
His hamstring injury came about in the 7-0 thrashing of Malaga last night in which he scored a hat-trick.
“Cristiano is an extraordinary player, and a great person,” added Di Stefano.
“He does things no one else does, and this makes people envious.”
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Alfredo Di Stefano- Jose Mourinho Defends Real Madrid; Cristiano Ronaldo Is Extraordinary