The World Cup runners-up had played down fears of Messi's injury in the lead-up to the friendly, but it ended up keeping the forward sidelined.
Martino revealed Messi was unable to put his boots on during training, due to swelling.
"Messi trained well during the first training session, he felt some pain during the second session, and could not put on his football boots during the third," he told a news conference.
"I understand people's anxiety to see him, but he just couldn't physically play."
A Nestor Renderos own goal and Federico Mancuello strike saw Argentina to their win against El Salvador at FedEx Field.
Martino was largely happy with his team's performance as they continue preparations for the Copa America.
"We had to have patience because there were no spaces. They settled well," he said.
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