Pekerman led Argentina in that tournament, opening with a 2-1 win over an Ivory Coast team that featured Yaya and Kolo Toure and goalscorer Didier Drogba.
Those star names are now accompanied by the likes of Gervinho and Wilfried Bony, who were on target to kick of the Africans' 2014 campaign with a comeback triumph over Japan.
Colombia top Group C having impressively dispatched of Greece 3-0 in their opener, but Pekerman is under no illusions with regards to the challenge his team faces when the two sides meet on Thursday.
"We are against a great opponent and we will have difficulties," he told reporters. "We have to face a very difficult game.
"In 2006, Ivory Coast debuted in the World Cup with lesser-known players. During that year there was a team little known, but a good one.
"Players have come together and joined the team; before it was good with Drogba, the Toure brothers…"
While Ivory Coast's squad has enjoyed time to mature together, Pekerman is also pleased with the strides his own playing group and staff have made.
"Colombia has always had a base of players, with a squad that has already been working for some time," he added.
"(The) team has grown in confidence. There is a bond between coaches and players, making solid team."
Playmaker James Rodriguez capped a fine individual showing with the superb goal against Greece and he wants Colombia to stay true to their possession style and chase victory in the face of a physically imposing opponent.
"Being next to great players makes it easy for you to play," he said.
"We have a tough game. They have good players, you have to be careful to try to win. A point is good but we always go out to win and (on Thursday) we will do the same."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.