Jose Pekerman's side produced their best performance at the tournament in the country's history by reaching the last eight, but their journey was to end as they fell to a 2-1 defeat to Brazil in the quarter-finals.
Rodriguez told reporters: "We are sad but very proud. The referee was wrong but Brazil is very good. David Luiz and Daniel Alves are great players.
"We wanted to carry on but we hold our heads high. Thank you Colombia. We're sad but we also have to feel proud because we left our skins out there."
Rodriguez netted his sixth goal of the World Cup in his side's defeat and currently leads the race for the Golden Boot.