The Gunners player connected with Raphinha's ankle and left him in need of treatment but the challenge went completely unpunished and Andre Marriner allowed the game to restart with a throw in. VAR made no recommendation to the referee to take a look at the tackle on his monitor.
Shortly after, Whites forward Joe Gelhardt connected with Takehiro Tomiyasu's ankle and was booked by Marriner, incensing Leeds and the home fans inside Elland Road.
Speaking on Sky Sports' Ref Watch, Gallagher insisted Xhaka should not have been sent off but felt Marriner did make a mistake.
"The VAR looked at it [Xhaka's challenge] to see whether it was a red card and decided it wasn't," he said.
"I don't think it is a red card, I think it's a yellow, but the problem there is VAR can't recommend a yellow card. He can recommend a red card or nothing. There's no intermediary.
"If he's sent to the screen, you're telling him it's practically a red card so there's a dilemma. It got overlooked on the pitch.
"Being consistent, I also think Gelhardt's challenge is a yellow card. What I would say is consistency is great as long as you're getting the right decision. It's not good if you make an error and compound that by making a second error."
VAR previously checked a challenge by Alexandre Lacazette on Adam Forshaw in the lead up to Arsenal's opening goal in the Elland Road clash but decided there was no clear and obvious error in Marriner's interpretation of the events.
Although the Leeds game was one of just four Premier League fixtures that took place, with Covid-19 outbreaks forcing postponements, controversy over officiating and VAR still reigned.
In the Liverpool game against Tottenham Hotspur, Harry Kane avoided being sent off for a studs-up challenge on Andy Robertson, who was later himself sent off after VAR intervention. Liverpool also felt they were denied a stonewall penalty for a challenge on Diogo Jota and Newcastle United were similarly aggrieved when Ryan Fraser was taken out by Manchester City goalkeeper Ederson without a spot-kick being awarded by the officials or VAR.