The South Americans took a 2-0 lead through James Rodriguez and Juan Quintero in the second half, but were forced to hold off the Elephants after Gervinho scored an excellent solo effort on 73 minutes.
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"I am very happy with the performance of all of my players," the 64-year-old Argentinian told reporters.
"We definitely do what we promise and we are never going to lack courage in games like that.
"I'm happy because we won a very difficult game. There was drama and that is the World Cup. We have many young players and we are working to reach a better level with the team."
Colombia have now all but qualified for the second round in their first World Cup appearance since France 1998 after adding to their 3-0 win over Greece last Saturday, but Pekerman refused to talk up their prospects.
"You can't assume anything until all matches are played," he said of Los Cafeteros' likely progress to the last-16.
"Colombia are feeling the pressure goes with that."
Pekerman's side face Japan on June 24 in their final Group C game.