Valdano has seen the opportunity to fire a new barb at Mou given his team's current struggles.
"Protesting is not something that Real Madrid should be doing," he told Cadena SER.
"No big club should be doing that. I saw that show on the other side, at Barcelona, for 25 years. I got the feeling that it weakened them on an institutional level and Real Madrid should not be giving out signals of weakness."
Valdano added: "Real Madrid are the biggest club of the 20th century.
"You shouldn't be putting so much emphasis on the result, why not defend the corporate and institutional culture of the club? I prefer the ideals of players and fans from the past. We must defend that prestige."