The Argentine has stressed he performed "a natural gesture", which was not aimed at either the crowd or coach, and says he is happy to clear things up.
The Argentina international grasped his groin as he was substituted, prompting fevered speculation that he was aiming an insult at either the crowd - some of whom booed him from the pitch for his performance - or coach Carlo Ancelotti.
Di Maria protested after the match that he was not making any sort of derogatory gesture and has now offered an apology to anyone who viewed the incident as such, with the club confirming it will look into the matter to see if any disciplinary proceedings should be required.
"I made a natural gesture when I was leaving. I did not do anything to the crowd, nor to the coach. It was a natural gesture that any man makes, especially when running," Di Maria, 25, told Real Madrid TV. "You do it on the pitch lots of times. If there is anyone who was made to feel bad then I apologize, but as I said, it was a natural gesture meant for no one. On TV, all you see is a millisecond. It's nothing.
"It's not that I stayed a long time to do something on purpose. It was something natural. For the people who feel bad for what I did, then I apologize, but it wasn't anything against anyone."
Di Maria added that he fully supported the club's investigation as he looks to clarify the incident.
"It seems right, not only for them to analyze it but for me to explain the situation and what happened," he said. "I think it's good to talk to them directly and explain what happened on the pitch, as I have already done to several Argentine radio stations."
Speculation has mounted that the player, already linked with a move away from Santiago Bernabeu after finding himself playing second fiddle to summer signing Gareth Bale, could be edging closer to the exit door after the incident.
However, the former Benfica man insists he is more than happy with life at the club.
"The truth is, I'm fine, apart from this issue, which makes me feel bad because of all the things that have been said and keep being said," he added. "I am very well and very happy. I still work in the same way and the coach relies on me.
"We have to continue like this, working, to get to the end of the year in the best way and in order to get the titles we want."