Martinez criticised the role of the official after the dubious award of a penalty following a challenge on Danny Welbeck. The former Swansea boss has been fined, but is awaiting the written outcome before deciding whether to appeal.
Speaking to Sky Sports, Martinez said: "We had the hearing and now we are waiting to see if we can appeal the decision because it is something I don't agree with.
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"At the moment it is one of those situations you have to accept but we will look into the written outcome and see if we can appeal it."
Martinez denies that his comments were aimed directly at Oliver, but more of a comment on the figure of the referee in away games against the top sides.
"If you see the comments they are not disrespectful comments at all to the referee. I wasn't talking about the referee, I was talking about the figure of the referee in those certain games.
"I was talking about the experience that we at Wigan Athletic have had going away from home and unfortunately the calls we have had of late.
"I would never question the integrity of the referee or question if the referee was biased towards a decision."
The written judgement is expected to come from the FA by Friday, but Martinez and his club will only have the weekend to decided whether to go through with the appeal or not.