The Argentina international was dismissed in the 77th minute of United's 2-1 quarter-final defeat at home to Arsenal after reacting angrily to being booked for diving.
Di Maria clasped at the back of Oliver's top, earning a second booking and his marching orders.
"In Spain he knows that he doesn't touch the referee, but that is also in his emotion," he is quoted as saying by BBC Sport. "I've already spoken with him, he knows my opinion but also I have to see on the video.
"I think he's touched the referee and that's forbidden in every country, so he has no excuses."
Having seen Wayne Rooney restore parity after Nacho Monreal had given Arsenal a first-half lead, United old boy Danny Welbeck settled the tie by pouncing on a weak Antonio Valencia backpass shortly after the hour mark.
And Van Gaal believes his team have nobody to blame but themselves for falling short in their most realistic bid for silverware.
"I said in advance that [a top-four Premier League finish] is a priority but as a manager, and as a player and club, you want to win titles and now we cannot win a title," he added.
"I've said in the dressing room we gave [the game] away by ourselves and that is the biggest disappointment. In the second half, we had the first chance also then we gave it away again.
"We don't lose from the opponent, we lost from ourselves and it was very disappointing. You play this match to win; to beat the opponent, we wanted to be in the semi-final."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.