The Red Devils won 5-3 on penalties in the FA Cup third round on Sunday afternoon.
Altay Bayindir was the hero as he saved from Kai Havertz during the shootout following a 1-1 draw at the Emirates Stadium.
Following the final whistle, United's official X account posted what appeared to be a thinly-veiled dig.
The one-word post simply read: "Justice."
United were reduced to 10 men and conceded a penalty during the initial 90 minutes in North London.
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Diogo Dalot was shown a second yellow card for a reckless lunge whilst his side were leading.
Arsenal grabbed an equaliser from the resulting corner as the visitors were forced to see out the match a man light.
Referee Andy Madley later awarded a controversial spot-kick to the home side after adjudging that Harry Maguire had fouled Havertz.
Martin Odegaard's resulting penalty was saved by Bayindir, though, to keep the score level.
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Arteta was asked after the match about the social media post from his opponents.
However, the Spaniard responded: "I comment about my team and my players."
The Gunners boss also felt his side deserved to win the match, despite failing to break the deadlock against 10 men.
He told the BBC: "It's unbelievable. Obviously, you measure the performance and what we did in relation to the position, you-know, you deserve to win the game by a mile.
"But the reality is we are out and the only thing that's going to be judged is that but internally I can't."
United's reward for their victory is a home tie against Leicester in the fourth round next month.