The Reds refused to give into the Uruguayan's demands to leave the club during the summer transfer window.
Suarez is now two games away from completing a ban for biting Branislav Ivanovic, and Rush said that the 26-year-old should look to the example set by Wayne Rooney at Manchester United.
"You only get so many chances and Suarez will learn from that," Rush told The Mirror. "[The fans] know that he always gives 100% and if he does that again they'll be singing his name again.
"United fans have had it with Rooney, but the way that Rooney played against Chelsea, he was all over the pitch, the fans appreciated that. They are not stupid.
"Maybe its exactly the same with Suarez. Liverpool fans have stuck by him previously and they can do it again. They still love him."
Arsenal failed with two bids to prise Suarez from the Merseyside outfit.