The Seagulls had Lewis Dunk sent off after only eight minutes as they were thumped 3-0 by Palace at Selhurst Park in December, but Poyet's men got their own back with a 3-0 win at the Amex in March.
Matches between the sides, who have been derby rivals since the late 1970s, are always lively affairs but with so much riding on them, Friday and Monday's encounters promise to be blockbusters.
Poyet said: "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."