The Real Madrid man wore the captain's armband at Craven Cottage, and assisted Carlos Bacca for Colombia's equaliser as they came from behind to win in London.
Pekerman said Rodriguez was already growing as a leader on the international scene.
"James Rodriguez has shown in recent times a high level of maturity for a 23-year-old, which is excellent," Pekerman said.
"He has assumed all the extra responsibilities he has had as captain in this game and the levels of expectation on him since the World Cup.
"He is always growing and today as captain, he knew how to manage the team.
"I think it was because of him that we recovered in the second half, he led the team well and played with great intensity.
"James was showing the way in the game to other players and showing the will required for us to win this match."
Pekerman talked down fears of a long-term injury for Radamel Falcao, claiming the front man is in the mix to play in Manchester United's clash with Arsenal on November 22.
"There is no doubt he is in optimal condition. He's recovered very successfully," Pekerman said.
"He done everything perfectly. This is a small muscular injury, it is different to the knee injury before the World Cup.
"He's in a good condition and could be ready for Arsenal. He hasn't even started yet.
"He will be one of the best players Manchester United have had and will break a lot of records in England."
Pekerman said Falcao's absence was a loss, but credited his side's depth for lifting past Jozy Altidore's early penalty.
"We'll always miss Falcao when he is not available to play," Pekerman said.
"However I know that we have very good players in this team and they have all performed well.
"Every player has got a good performance in them, but Falcao, he always performs well and the high ranking of the team has a lot to do with him.
"We expect him to be back with us soon."
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