"If a player speaks about you and your team-mates like this, you feel offended," Iniesta told Onda Cero.
"I'm not theatrical in any way, and neither are the other guys. These comments hurt because they are a personal attack."
But Pepe was unmoved as he spoke at a Portugal press conference before the upcoming World Cup qualifiers against Russia and Northern Ireland.
"If someone is offended it is because the truth hurts," Pepe said. "I just said what really happened in the game."