Following a narrow 1-0 defeat to Manchester City on Saturday, the Eagles continued their winless run in the competition.
They nevertheless came close to claiming a point against the reigning Premier League champions, however, after doing so against Manchester United, Newcastle United, Brighton & Hove Albion and Liverpool in recent weeks.
Palace’s performances have not always yielded the results they have warranted this season, but with away games against Brighton and Arsenal to come in the next seven days, Milivojevic has vowed to fight for every point.
“It’s not very comfortable at the moment, because we know the next two games are very hard,” the captain noted, speaking after Saturday’s match.
“We play two away games, Brighton and Arsenal – but we’re here to fight.
“We have a good squad, a talented squad. We have a mixture of experienced and young, talented players, so I think we’re going to use that until the end of the season, and hope to reach our goals.”