Adrian Lopez and James McCarthy both limped out of the 2-1 loss to Norwich City on Saturday to take the Latics’ injury list to eight.
Martinez accused the Canaries of targeting McCarthy, leading him to damaging his ankle, and revealed that both are doubts for the visit of Arsenal on December 22.
And the manager is hoping his charges will step up their efforts to compensate for certain absentees: "We don’t want to look at excuses but having so many players unavailable, and senior players at that, is affecting us too much at the moment.
"It’s a situation I’ve never seen before: Adrian Lopez picked up a nasty hamstring injury and James McCarthy was involved in one of the most infuriating incidents of the game having been targeted by the opposition and picking up a nasty ankle injury as a result.
"I doubt James will make the Arsenal game next weekend and we’ll have to assess Adrian in the week but he’s a doubt as well.
"Now is a moment that we need to get together as a club and face this adversity to make sure we find a response.
"Having eight players missing is a real challenge for any club but we need to show now our typical togetherness and that feeling only we can create at the club."
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He continued: "We are disappointed with the first-half performance, didn’t get to grips with the game and gave a really soft goal away early on.
"It wasn’t anywhere near good enough but the reaction is what pleased me the most. After the break we showed real intent, started to be ourselves and scored an outstanding goal from open play.
"At that point we had the momentum and if anything looked as though we could get a winner but the disappointment once again was the conceding of another soft goal, giving the smallest player on the field a free header inside the box. Conceding goals like that make it very difficult to get anything from games and we need to improve upon it."