The duo picked up injuries in the home defeat to Swansea on Sunday and have already been ruled out of the clash with Manchester City in the Capital One Cup.
Besic has a hamstring injury and Mirallas a knee problem and both are now struggling, but how long they will be out for is uncertain.
"It's hard to tell [the seriousness of both injuries]," Martinez said.
"Muhamed Besic injured his left hamstring - the opposite leg to the problem he had recently."We will also assess Kevin Mirallas, who injured the tendon in his right leg around the knee.
"I don't expect them to be fit for Wednesday and I expect a bit of a period where they will be unavailable. It is a real shame because both players gave us a really refreshing look and reached good levels at this stage of the season."