The two teams have a storied rivalry dating back to the 1970s, but ahead of the first leg at Selhurst Park on Friday, Poyet hopes that nothing "silly" occurs during the fixture.
The 45-year-old told reporters: "We need to make it about being a football game, only thinking about football and nothing silly.
"Over the two matches it could be two magnificent games of football. Let's not do anything silly because it's not worth it.
"Let's remember it's about who plays better on the day and nothing else - and accept that."
The winner of the two-legged tie will face either Watford or Leicester City for a place in the Premier League.