The forward took his tally for the tournament to five goals, topping the Golden Boot standings, and the coach admitted Colombia's hopes rest on the Monaco man
The Monaco forward's double - his fourth and fifth goals in four games - in Colombia's 2-0 win over Uruguay on Saturday helped them reach the quarter-finals for the first time.
Pekerman admitted his whole World Cup plan revolves around James and has been increasingly impressed with how the 22-year-old, who is now top of the Golden Boot standings, has embraced the burden of leading Colombia's charge for the trophy.
"James has been essential, he's been fundamental in the team," the coach told reporters. "We had good performances in all positions but he’s given a lot.
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"I’ve had extraordinary football players in my teams before - elite players of a very high technical level. I placed everything in James’ hands because I saw an extraordinary talent.
"What is surprising is he has no problem taking the responsibility at his age. Football forces you to deal with situations. We have a technically gifted player who has everything to be a top-notch player at world-class level, and who can interpret what I need to be done with the team.
"I greatly praise what he’s doing and I never had any doubts that this was going to be his World Cup."
Pekerman was proud of how his players nullified Uruguay's threat, especially how they reacted in the latter 45 minutes when the Celeste were chasing the game after James' stunning first-half opener.
"We’re very happy with everything that happened tonight," he added. "I believe the match was very difficult for us. We knew who we were playing against but the team was very concentrated and we played a wonderful first half.
"Uruguay know how to play these matches very well, they always have the capacity to handle the 90 minutes. We had to handle the ball and do this skilfully, to create concern and disturb them. Good players also made a difference and we were able to come out with an advantage at half-time.
"As expected, Uruguay stepped it up in the second half so we hit back with a good goal and that was also very positive. After that Uruguay, with their fresh substitutes, played well and we had to step back because of that, but we always kept the calmness you need in these matches."
Pekerman is expecting a classic when Colombia face host nation Brazil - who narrowly overcame Chile in a tense penalty shoot-out after a 1-1 draw in Belo Horizonte - next Friday.
"It’s going to be a great match," the Argentine continued. "We're two teams which have players with the intention of playing properly.
"Brazil will be at their best. They've just played a very difficult match but winning gives you a lot of confidence. We can expect a match with a lot of tension but also a good technical level because of the attitude of the teams.
"Yes, we will always respect Brazil because they are a great team with great players. We know everyone at the World Cup goes through difficult moments but they’ve overcome them."