The German says that the defender's behaviour in Wednesday's Clasico does not reflect what type of man he is off the field but reckons the Portuguese goes too far sometimes
The Portugal international appeared to stamp on Lionel Messi's hand during his side's 2-1 loss to Barcelona in the first leg of their Copa del Rey quarter-final at the Santiago Bernabeu on Wednesday.
Schuster, who coached Pepe in 2007-08, stressed that the defender is "a different person" off the field and noted that the former Porto man's billing as an aggressive player began when he kicked Javier Casquero twice in a league match in 2009, an action which earned him a 10-game ban.
"I do not need to say how good Pepe is, how a great person and professional he is, or that he has to be at Madrid," Schuster told Marca.
"What he did was ugly, but this is all because we can watch everything that happens on the pitch.
"Migueli, [Fernando] Hierro, [Roberto] Ayala, these are players who hit hard, but now we can watch everything.
"Since the day of the incident with Casquero, I do not know what has happened with Pepe. It is something rare, something you cannot explain if you know him.
"When Pepe puts on the shirt, he is a different guy. Jose Mourinho knows how to take advantage of these things, but sometimes he goes too far."
The 52-year-old coach, who is currently out of work, then admitted he was surprised with Mourinho's formation in Wednesday's match.
"There are some things that are hard to understand," Schuster added. "[Ricardo] Carvalho had not been playing in a long time, [Hamit] Altintop perhaps does not improve the team's level and Pepe played again in midfield.
"But most of all, what happens when you change so many things is that you are taking many risks.
"Barca have been playing in the exact same way since I left Madrid, but Madrid try to change things in every Clasico.
"There is one team which plays always the same every year and another who tries the impossible to win."