Hodgson, who has guided the Eagles from the bottom of the Premier League up to 14th since taking charge in September, was unimpressed by VAR when he first witnessed the technology at the 2017 FIFA Confederations Cup in Russia.
"I experienced it during the Confederations Cup, albeit from a television studio," Hodgson told reporters.
"It was chaotic there... it didn't work very well at all, because the communication between the referee and the guy on the machine wasn't working well.
"There are a lot of questions to be answered with regard to how things can dovetail together, but if they can get it to dovetail together, and it stops gross injustices, then on our side of the fence, we'd be all for it."
VAR involves assistant referees watching the action remotely and then drawing the match official's attention to mistakes or missed serious incidents.
The technology will be limited to four potentially game-changing situations: helping referees reduce errors on goals, penalty decisions, red cards and cases of mistaken identity.
Palace were unfortunate earlier this campaign when Everton's Oumar Niasse won a dubious penalty in a 2-2 draw at Selhurst Park.
The striker received a retrospective ban for diving but it did little to help Palace, who dropped two points due to the on-field decision. Hodgson said under such circumstances VAR's flaws could be exposed.
"How many times are you going to need to see the incident before you can have an opinion?" he asked.
"We can't come to a conclusion because one person will say 'Definitely yes,' one will say 'Definitely no'. How are we going to get to a stage where we only use it for the gross injustices? That's my fear."