The Gers fell behind on the 25-minute mark courtesy of a superb volley from Celtic's Paulo Bernardo, before they appealed for a penalty on the stroke of half time following an apparent handball inside the area from Alistair Johnston.
Under pressure from Rangers forward Abdallah Sima, Celtic right-back Johnston attempted to shield the ball out for a goal kick before appearing to swat the ball away from Sima's chest with his right hand.
According to Sky Sports News, VAR looked at the incident, but the officials did not consider Johnston's hand movement to the ball to be unnatural.
A goal kick was eventually given by on-field referee Nick Walsh, but it later emerged that Sima was offside in the build-up, so the decision ultimately proved irrelevant.
Nevertheless, Sky Sports claims that Rangers will request for a copy of the VAR audio of the incident from the Scottish FA.
A Rangers spokesperson said: "Rangers have asked the Scottish FA to make the VAR audio available to the club to understand why no penalty was awarded despite a clear hand ball by Celtic's Alastair Johnston.
"The club is keen to understand the process that led to that decision being made as it was not made public at the time, nor communicated to our team. Rangers remains advocates of VAR, but there must be significantly more transparency for it to be successful in Scotland."
Rangers went on to conceded a second two minutes after the break when Kyogo Furuhashi fired a stunning strike into the top corner, and salt was then rubbed into the visitors' wounds when Leon Balogun was shown a straight red card for dragging down Daizen Maeda as he raced through on goal.
James Tavernier pulled one back for the Gers with a brilliant free-kick two minutes from time, but they were unable to find an equaliser as Philippe Clement suffered his first defeat in his 17th game in charge of the club.
Clement vented his frustration at the controversial penalty decision after the match and also felt that Celtic's Bernardo should have been sent off for a late tackle on Connor Goldson when he was already on a booking.
Speaking to Sky Sports reporter Luke Shanley, Clement said: "We played 15 minutes with 10 players, and that was the right decision, it's a red card. We didn't do that action well.
"But I have other questions also about, why not a handball in the first half to get a penalty? It's a clear handball.
"Why not a second yellow card for some tackles and then at the end of the game a lot of yellow cards? A few strange decisions in that way."
Clement was then told by Shanley about the offside in the build-up to Johnston's alleged handball, and the Rangers boss replied: "The decision was not made about an offside, the decision of no penalty was made about the handball. That was the decision. So that was a strange decision for me."
The Belgian added: "We were unlucky with the two [Celtic] goals and if we get this penalty, it's a 2-2 with the quality of the game. It's another story in perception."
Defeat for Rangers leaves them sitting second in the Premiership table, eight points behind Brendan Rodgers's Celtic side at the summit, but Clement's men have two games in hand, with a home clash against Kilmarnock up next on January 2.