The Russian side travel to Anfield for the second leg of their Europa League tie leading 2-0, and Aldridge wants the fans to be the "12th man".
"Brendan Rodgers's side need the 12th man from the first minute until the last," Aldridge said in his Liverpool Echo column.
"The fans need to intimidate Zenit and the officials. That noise will inspire Liverpool and could make the Russians crumble.
"I can't really remember a really special atmosphere at Anfield this season and it's time to put that right against Zenit St Petersburg on Thursday night."
Liverpool will be without January signings Philippe Coutinho and Daniel Sturridge for the game.