Cardozo was overlooked by coach Gerardo Martino for the 2011 Copa América squad, despite scoring 23 official goals for Benfica in 2010–11. Having already been included by Ramón Díaz in the "Albirroja" preliminary squad, Cardozo would again miss out 2015 Copa América due to a back injury. On 16 June 2019, aged 36, he scored against Qatar in Copa América and became the oldest player in Paraguay's history to score in that competition, breaking Delfín Benítez Cáceres' 1946 record.