Colombia coach Jose Pekerman announced on Monday that the trio had missed out on being part of the World Cup finals in Brazil with Falcao failing to prove his fitness after knee surgery in January.
Perea also missed out due to an injury, while Muriel was deemed surplus to requirements, as Pekerman picked four strikers - Jackson Martinez, Carlos Bacca, Adrian Ramos and Teofil Gutierrez - ahead of the Udinese forward.
"I found this decision hard," Pekerman said of Muriel's omission.
The trio of unhappy players fronted the media alongside Pekerman in Cardales, Argentina, on Monday.
Falcao revealed he had admitted to the Argentine coach he was not 100 per cent fit and ruled himself out of the tournament, so he would not deny a fully fit teammate.
"I was personally very excited to participate but we must carry on and support the team from the outside," the Monaco striker said.
With Falcao finally ruled out of the upcoming World Cup, there will be plenty of pressure on Porto's Martinez, Sevilla's Bacca, Ramos of Borussia Dortmund and River Plate's Gutierrez to score goals in Group C versus Greece, Ivory Coast and Japan.
The absence of Perea due to an ongoing groin injury means Milan's Cristian Zapata, Mario Yepes of Atalanta and San Lorenzo's Carlos Valdes will be Pekerman's main central defensive options in Brazil.
Pekerman named seven defenders, nine midfielders, four strikers and three goalkeepers in his final squad.
Squad in full:
Goalkeepers: Faryd Mondragon (Deportivo Cali), David Ospina (Nice), Camilo Vargas (Santa Fe)
Defenders: Santiago Arias (PSV), Pablo Armero (West Ham), Eder Alvarez Balanta (River Plate), Carlos Valdes (San Lorenzo), Mario Yepes (Atalanta), Cristian Zapata (Milan), Camilo Zuniga (Napoli)
Midfielders: Abel Aguilar (Toulouse), Juan Guillermo Cuadrado (Fiorentina), Fredy Guarin (Inter Milan), Victor Ibarbo (Cagliari), Alexander Mejia (Atletico Nacional), Juan Fernando Quintero (Porto), Aldo Leao Ramirez (Atlas), James Rodriguez (Monaco), Carlos Sanchez (Elche)
Forwards: Carlos Bacca (Sevilla), Teofilo Gutierrez (River Plate), Jackson Martinez (Porto), Adrian Ramos (Borussia Dortmund)
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
