Pena was forced to make way for captain Paolo Guerrero, who has been freed to take part at the tournament after the Swiss Federal Tribunal agreed to temporarily lift a 14-month doping ban pending an appeal.
Guerrero, who tested positive for a cocaine byproduct contained in a tea and which he said he ingested unknowingly, was freed to take part on Thursday and scored twice in the 3-0 win over Saudi Arabia on Sunday.
Peru, making their first appearance at the World Cup since 1982, face Denmark, France and Australia in their group.
"This is the most difficult moment of my career and I feel I did not do enough to take part in the best competition in the world and represent my country as well as possible," Pena said on Instagram.
"Tomorrow, I will wake up with more strength than ever and continue what I love doing," added the 22-year-old, who plays for Spanish second division side Granada.
Peru squad:
Goalkeepers: Pedro Gallese (Veracruz), Carlos Caceda (Deportivo Municipal), Jose Carvallo (UTC).
Defenders: Aldo Corzo (Universitario), Luis Advincula (Lobos Buap), Christian Ramos (Veracruz), Miguel Araujo (Alianza Lima), Alberto Rodriguez (Atletico Junior), Anderson Santamaria (Puebla), Miguel Trauco (Flamengo), Nilson Loyola (Melgar).
Midfielders: Renato Tapia (Feyenoord), Pedro Aquino (Lobos Buap), Yoshimar Yotun (Orlando City), Paolo Hurtado (Vitoria Guimaraes), Christian Cueva (Sao Paulo), Edison Flores (Aalborg), Andy Polo (Portland Timbers), Wilder Cartagena (Veracruz).
Forwards: Andre Carrillo (Watford), Raul Ruidiaz (Morelia), Jefferson Farfan (Lokomotiv Moscow), Paolo Guerrero (Flamengo).
(Writing by Brian Homewood; Editing by John O'Brien)
