Players at Palace know how much their talented teammate is targeted by the opposition with fouls and aggression.
And Milivojevic believes that it is up to him to lead by example and ensure that Zaha is protected throughout matches.
"It's true," he told the club website.
"We all know that most of the teams will go to kick your best player – I try to protect [him] – it's part of my job as captain. I'm always there to help others."
Palace are on a winter break, but they hope to end a run of games that has seen them without a win since Boxing Day.
They are only six points clear of the relegation zone as things stand.