United went on to lose 2-0 to the Ligue 1 champions, with the damage done by Presnel Kimpembe and Kylian Mbappé in the second half.
Ole Gunnar Solskjaer’s side must now turn the tie around in Paris next month in order to reach the Champions League quarter-finals.
In his post-match press conference, Solskjaer confirmed that Lingard and Martial had suffered hamstring and groin injuries respectively.
However, the United caretaker could not discuss the severity of their problems or put a timescale on their return.
United travel to Chelsea for an FA Cup fifth round tie next Monday night before Liverpool visit Old Trafford in the Premier League the following Sunday.
“You don't know,” Solskjaer said, when asked for a prognosis on Lingard and Martial. “Muscular injuries, hamstring and groin. We'll need a couple of days to assess them.”
Lingard was replaced before half time by Alexis Sanchez, while Martial was substituted during the break for Juan Mata.
Neither replacement managed to help United turn the first leg around once PSG went ahead and Solskjaer admitted that losing Lingard and Martial was a blow.
“That's the reality,” he said. “Jesse and Anthony are big parts of our squad. They’ve played really well.
“Second half we didn’t have so much movement and pace to get in behind. Juan got on the ball for us and created a few bits. We need to find a different way to play when Anthony and Jesse are out.”
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