We are yet to prove ourselves, says Pekerman
Pekerman's men are preparing for Thursday's FIFA World Cup Group C fixture against Ivory Coast, where a win would all but secure a spot in the last 16 after their opening round win against Greece.
Colombia finished second in CONMEBOL qualifying, two points behind Argentina en route to Brazil.
But speaking on the eve of their match in Brasilia, Pekerman insisted qualifying for the World Cup and playing against countries from other continents were completely different tasks.
"The South American qualification towards the World Cup is one thing, and the World Cup itself is another one," Pekerman told reporters.
"The diversity of styles is very varied within the national teams.
"We know each other better in South America, because we play frequently. But the World Cup brings many changes."
If Colombia reach the second round it will be just their second appearance in the knockout stage, their previous coming in 1990, though Pekerman is preparing for hurdles along the way.
Three countries from each four-team group progressed to the knockout rounds in Italy and Colombia went on to make the round of 16, before bowing out to Cameroon 2-1 after extra-time.
"We have seen it in every team that has won a World Cup or have reached the very final states of a World Cup, they have had ups and downs, difficult matches," he said.
"Champions always got through difficult moments. That's what history says. We have to go very long time ago to see a team like Brazil in 1970 or Germany in 1974, those teams that maybe dominated since the very beginning of the tournament.
"But I trust this age is gone. Today there is much more equilibrium. We can see it on every match, that the favourites have difficulties in spite of his quality.
"I think to be aware of this situation is a synonym of growing up. I always valued the Colombian players I coach today because they know how this works."