The talented duo were forced to sit out the second half of the first leg of the round-of-16 tie, with Alexis Sanchez and Juan Mata taking their place.
Lingard pulled up after sending the ball wide to Martial on the break towards the end of the first period, while the Frenchman sustained his problem earlier in the proceedings but soldiered on until the interval.
With more big games on the horizon, starting with the Emirates FA Cup fifth-round clash at Chelsea next Monday and the next Premier League outing against Liverpool at Old Trafford on 24 February, there must be concern about the availability of two key members of Ole's squad.