Colombia – third seeds in Friday's draw – will face Greece, Ivory Coast and Japan in Group C, and Pekerman insists they can make it to the knockout stages for only the second time.
The 64-year-old guided the South American nation to the finals after replacing Leonel Alvarez in January 2012, and will be managing a side at the finals for the second time after leading Argentina in 2006.
With no clear favourite in the group, Pekerman hopes his side can stamp their authority and progress.
"We hope to do well," he told Telam. "The guys did a great job in qualifying, but it has passed.
"I think it will be a very even and attractive group.
"We trust that we have the potential, but the people of Colombia have to understand that a World Cup is something different."
