Television pictures showed Spence bleeding from a cut to the back of the head after being felled by an object thrown from a section housing Rangers supporters.
Local media said Rangers would work with Livingston and Police Scotland to identify the culprit.
"I don't think that belongs in football, does it?" Gerrard told reporters after the game, which Rangers lost 1-0.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I think we all know that’s not right. He’s trying to do a job so that's not right."
A professional trade union for senior football referees in Scotland condemned the incident and called on the Scottish Football Association (SFA) to launch an investigation.
"We strongly condemn the unacceptable incident at today's game. This cannot be tolerated," Prospect Scotland Football Referees Branch said on its Twitter page.
"We call on the @ScottishFA to carry out an urgent full investigation. Referees & officials are entitled to a safe workplace, free from intimidation and violence."
Livingston's shock win saw them move above both Rangers and champions Celtic into third place in the table.
(Writing by Peter Rutherford in Seoul; Editing by Ian Ransom)
