The 48-year-old admits that the Portuguese could be sanctioned by the club, but asserts that he has been targeted
The Portuguese defender was widely criticised for his boisterous performance in Wednesday's Clasico, which featured a stamp on Barcelona's Lionel Messi.
However, Butragueno has stated that Pepe is not a bad person, and has been targeted due to his athletic ability.
"Pepe is a nice guy and very passionate. He has suffered because he's a good athlete," Butragueno said according to Sport.
However, the 48-year-old remained tight-lipped as to whether Pepe would receive censure from the club for his performance.
"We have an internal system," he explained. "Much has been said over him, and we are no going to participate with the public discussions. It's something that will be discussed amongst ourselves."
The director, who represented Real Madrid as a player, has also asserted that his side's defence of the Copa del Rey title is far from over, despite a 2-1 deficit after the quarter-final first leg.
"The tie is not over yet. You will se us fight for this shield," he vowed.
Real Madrid and Barcelona square-off once more on Wednesday at Camp Nou, with Jose Mourinho's side needing at least two goals to progress to the semi-finals of the competition.