Van Gaal's dream of landing a trophy in his first season at Old Trafford went up in smoke as United lost 2-1 to the Gunners on Monday night.
The hosts ended the game with 10 men after the latest episode in Di Maria's disappointing Red Devils career unfolded in the 77th minute.
After being cautioned for simulation, Di Maria remonstrated with referee Oliver and then grabbed his shirt and yelled at the official when he had turned his back on him.
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Replays showed the first booking on Di Maria may have been harsh and Aaron Ramsey had pulled the player back, but the £59.7million man's actions thereafter deserved sanction, according to his own manager.
"I think he's touched the referee and that's forbidden in every country, so he has no excuses," the United manager said.
"In Spain he knows that he doesn't touch the referee, but that is also in his emotion.
"I've already spoken with him, he knows my opinion but also I have to see on the video.
"He doesn't have to touch the referee. That is not so smart of him."
Angel Di Maria pulls at the shirt of the official
Di Maria actually started the game reasonably well, setting up Wayne Rooney for an equaliser with a wonderful curling cross.
But his dismissal clearly angered his manager and the player himself, who refused requests for an interview post-match.
When asked whether he would discipline Di Maria, Van Gaal said: "No, I don't think so."
The Dutchman admitted United handed Arsenal victory on a plate with the second goal.
Antonio Valencia, who had been the best United player on the pitch, according to Van Gaal, sold David de Gea short with a poor back-pass, leaving Danny Welbeck to knock the ball past the goalkeeper and into an empty net.
"I think it is very disappointing when you give the victory (away)," Van Gaal said.
"You doesn't lose (because of) your opponent - you have lost (because of) yourself. That is very disappointing."
Angel Di Maria reacts during the defeat to Arsenal (GETTY IMAGES)
When asked whether he stood by his decision to sell Welbeck and stick with Wayne Rooney, Robin van Persie and Radamel Falcao last summer, the reply was emphatic.
"Yes," Van Gaal said bluntly.
"A lot of times against the club who a player was playing for (he) shall be very motivated, but I think we gave that goal (away)."
When it was put to him that Falcao, who did not make it off the bench, had flopped this season, Van Gaal fired another retort back.
"He has scored four goals and (has made) three or four assists," he said. "And he stimulates also the other players."
Arsene Wenger said he expected Welbeck to be fired up for the game, given that he was facing his old club.
"We want all to do well when we play against our former club to show we are great players," the Arsenal manager said.
"It is not easy to deal with the mental aspect of it."
Arsenal will face either Reading or Bradford in the semi-finals.
PA
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