Wayne Rooney cancelled out Nacho Monreal’s opener but Danny Welbeck netted a winner late on to secure Arsenal’s progression into the semi-finals of the competition.
Angel di Maria was also sent off by referee Michael Oliver to compound a miserable evening for United.
However, van Gaal refused to blame the officiating for the loss and said United lost the game due to their own poor performance.
Speaking about the result, van Gaal said: ”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.”
As so often has been the case this season, United struggled to finish their chances.
Marouane Fellaini, Ashley Young and Di Maria all missed good opportunities and United can have no complaints about the result. Fans will be doubly frustrated that it was Welbeck who knocked United out of the Cup after he left Old Trafford for London in a £16m move last summer.