Pepe has come under heavy criticism for appearing to stamp on Lionel Messi's hand during Wednesday's 2-1 loss to Barca in the first leg of their Copa del Rey quarter-final at the Santiago Bernabeu.
"I do not have a team-mate like Pepe in Barca's dressing room," Pique said during a press conference. "But everyone saw it, everyone.
"I do not hope to have a team-mate who acts like Pepe does."
Pique went on to declare that he hopes the Spanish Football Federation's Disciplinary Committee will analyse the incident.
"The referee may or may not have seen it, but there are people whose job it is to handle these cases," he added.
"There is TV footage. If they do their job well, we will see what they decide."
Questioned about Pepe's action after the match, Madrid coach Jose Mourinho noted he did not see the incident, but admitted that the former Porto defender could be disciplined by the club if he stood on Messi's hand intentionally.
Pique also praised Messi, remarking that the diminutive attacker is a role model, both on and off the field.
"Besides what he does on the field, one must thank Messi's human quality," Pique affirmed.
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