Pogba, 22, hurt his right hamstring early in Juve's 3-0 demolition of Borussia Dortmund, which saw the Serie A title-holders advance to the UEFA Champions League quarter-finals.
The France international is set to miss up to seven weeks, which would rule him out of competing in either legs of the quarter-finals or semi-finals in Europe.
The injury will see him miss friendlies for Deschamps' France, against Brazil and Denmark in March.
"What happened is difficult for the player himself," Deschamps said on Thursday.
"Paul has his first muscular injury, that's something new for him.
"Even when a young player is fit, these kind of things can happen.
"He's playing a lot of games. The seasons are long for him; he doesn't always have a real holiday. His body needed a break."
Uncapped Chelsea centre-back Kurt Zouma was called up by Deschamps, who said there was no extra burden on defensive duo Raphael Varane and Mamadou Sakho.
Varane has started just 14 times for Real Madrid this La Liga season, while Sakho has started in Liverpool's Premier League XI on 12 occasions.
Deschamps said he was happy with the defenders at his disposal.
"Raphael has played a lot of games. I am not only reading articles in newspapers, I am watching all the games. It depends also about his team," he said.
"For me, Raphael and Mamadou are as good as they were in Brazil [at the World Cup].
"Sakho has been injured and came back. He's now competitive again."
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