The former Manchester United winger was in talks with Pumas as he was leaving AEK Athen, but eventually signed with LigaMX rivals Monterrey last week.
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Pumas say they had a deal in place with AEK and were expecting Martial in Mexico City to sign forms before the Frenchman's camp pulled out of talks.
Miguel Mejia Baron, a member of the recruitment team at Pumas, told TUDN: "It's not the agent who decides, it's the player. I don't know if it is because of money - maybe he analysed other situations and had every right to make his decision.
"Maybe what he lacked was an apology."
Martial could make his debut for Monterrey today against Club America.