The Eagles exceeded the majority of expectations last season when they finished in 11th place in the table.
While revealing that manager Tony Pulis is keen to guide the team into the Europa League, Parish believes that cementing their place in the top flight is the main priority this season.
"I think we need to focus on staying in the league for now. The Europa League really took its toll on sides like Swansea last year, it dragged them down to the bottom," he told Sky Sports News.
"Tony tells me it's a great adventure and if we got there we got there, but I think right now we need to focus on staying in the league, that's a priority."
Palace play their first match of the new Premier League season on Saturday when they face Arsenal at the Emirates Stadium.