Di Maria, who was replaced by Gareth Bale midway through the second half at the Bernabeu and was whistled by the home fans as he trudged off, insisted it was "a natural gesture" and said he apologised if anyone had found it offensive.
The incident was widely debated in the Spanish and Argentine media on Tuesday and prompted further speculation that Di Maria, who has made fewer appearances since the arrival of world record signing Bale, might be sold either in the January transfer window or at the end of the season.
"I did not want to do anything towards either the supporters or the coach as was being claimed," the 25-year-old was quoted as saying on Real's website (www.realmadrid.com) on Tuesday.
"It was a natural gesture that any man does, and all the more so when he is running," he added.
"You do it a lot on the pitch. On television you can see that it lasts a millisecond. It's nothing.
"It's not like I was doing it on purpose for an extended period of time."
Di Maria said he was "in very good shape and very happy" at Real and that coach Carlo Ancelotti had faith in him.
He added that he agreed with the club's decision to launch an enquiry as it would help resolve the matter.
"I think it is right, not only for those who have opened the enquiry but also for me so I can explain the situation and what it (the gesture) was," he said.
(Reporting by Iain Rogers, editing by Ken Ferris)
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