The Colombians, who suffered a 2-1 loss on Friday night, had a number of decisions go against them in Fortaleza.
While suggesting that the officials were not always fair, Rodriguez insists that he and his teammates can be proud of their run at the tournament.
"We have not progressed to the semi-finals. The referee did not always whistle in the right direction and did not penalise many of Brazil's misdemeanours but we go out with our heads held high," he is quoted as saying by Goal.com.
Rodriguez currently leads the Golden Boot standings at the World Cup with six goals in five games.