Martinez released a statement on the site, confirming Alcaraz had said sorry to him personally for the episode and that an apology had already been made to Wolves.
"The player has apologised to me and has accepted that he did wrong," Martinez said.
"The incident does not reflect the normal character of someone who takes his responsibilities very seriously.
"Antolin is a special character and a big asset for our squad and you would never normally see him associated with that sort of behaviour.
"Unfortunately, he lost control of his actions due to the importance of the game and the frustrating nature of our performance on the day, and even though they were mitigating factors, spitting is not an action that should be associated with any ambassador of Wigan Athletic.
"He clearly cares with his life for every Wigan Athletic result. He's a true professional and in this incident has reacted wrongly due to a combination of anger, frustration and cultural differences.
"I know he never meant to spit on an opposing player but he will learn from his actions.
"We have already apologised to Wolves and we are ready to draw a line under it.
"All of our foreign players need to understand the culture of the country they are playing in, and the seriousness of what certain actions mean in England, whatever the provocation."