Carballo appeared reluctant to show yellow cards for much of the match, despite a huge number of fouls, with Colombia left particulary frustrated that a number of heavy challenges on James Rodriguez went unpunished.
Carballo also opted against showing Julio Cesar a red card when he brought down Carlos Bacca in front of goal for the penalty which James scored in the closing minutes - another decision which prompted a furious response in the Colombian press.
And Falcao, who missed the tournament in Brazil after failing to recover from a knee injury, was left deeply unimpressed by the officiating in Fortaleza.
"For the next game, remember to call the referee, because he did not show up today," he wrote on his official Twitter page.
Falcao also wished Neymar a quick recovery following the back injury which has ruled him out of the rest of the tournament and praised his compatriots for their efforts over the past month.
He said to Neymar: "Best wishes for a speedy recovery", before adding to his team-mates: "Thank you for what you have done, the best is yet to come."
Goal understands, meanwhile, that Falcao has agreed personal terms ahead of a proposed move to Real Madrid, though a fee is yet to be agreed.