Pique caused a storm this week when he hit out at the European champions for their "values" and alleged influence from the Madrid "box seats" over the treatment of Lionel Messi and Neymar in their ongoing legal cases with Spanish financial authorities.
Perez, speaking at a sponsor's event on Thursday, pointed to Madrid's sporting success as a way of responding.
"Welcome to a place where the only things that matter are sporting values," he told the media.
"Here today are the [football and the basketball] squads, which have 20 European Cups between them. Because of them, our club is respected, but our club is also respected for the principles and the values which are in its DNA."
Pique, speaking after Spain's 2-0 friendly win over France in Paris, appeared to have taken exception to the images that appeared in the Catalan press of public prosecutor Marta Silva seated in the Madrid directors' box at the match against Real Sociedad.
Silva - a former Madrid board member who regularly attends matches - is reported to have pushed for a stern punishment to be handed down to Messi, who is appealing against a 21-month prison sentence for tax fraud.
Madrid star Cristiano Ronaldo was similarly accused of evading taxes by Football Leaks, although his agent's management company Gestifute strenuously denied any wrongdoing.
"I don't like the values Real Madrid transmit, although there are players there I really appreciate and am friends with," Pique said.
"What I don't like about Real Madrid is how those in the box seats pull the strings. The person who accused Messi and Neymar and who has a different treatment for Cristiano is in those box seats."
Barca vice-president Jordi Cardoner came to Pique's defence, insisting that the Spain international was simply being honest.
"Gerard Pique has not told a lie and Barca will always be on the side of the truth," he was quoted as saying by La Vanguardia.
"The truth does not have to start a conflict. From what I heard, Pique expressed a free opinion and exercised his freedom of expression. He didn't disrespect anyone. He has spoken clearly and at times that clarity can offend."
La Liga president Javier Tebas, meanwhile, told Marca: "Pique made a mistake, that's all. I don't think his comments generate violence but tension."