Pekerman: Colombia never lost faith
Thiago Silva gave the host nation the lead in the seventh minute, before David Luiz struck with a superb free-kick midway through the second half to double their advantage.
Tournament top scorer James Rodriguez pulled one back from the penalty spot 10 minutes from time, but Brazil will go on to face Germany in the semi-finals.
Despite defeat, Pekerman was proud of his players' will and determination, claiming they never allowed Brazil to relax or sit on their advantage.
"We always had the illusion of being able to win this game," he said. "This team did much for Colombia because football is valued.
"We aspire to win always.
"I believe that Brazil were always concerned about our players"
Speaking of Rodriguez, who ends the tournament with six goals to his name, Pekerman said Colombia's elimination also brought an end to the involvement of "one of the best players in the world".