The South Americans, who have not appeared at the tournament since France 1998, begin their Group C campaign against Greece on Saturday - a game head coach Pekerman expects to be difficult.
Colombia are shorn of their leading light with striker Radamel Falcao missing the competition through injury, but Pekerman is hopeful they can do the country proud.
"Expectations are high again and there is pride that Colombia are participating in a World Cup after so long," he said.
"We have always been a tight-knit group, a real family. The team takes on the challenge.
"We will face a tough opponent (Greece)."