The elegant No. 8 also warned that even if Stade beat Racing at the weekend, they will be far from guaranteed a play-off place with a final game away to a resurgent Biarritz.
He said: "If we lose we are on holiday. If we win we can still qualify for the play-offs. We also know that even if we win we aren't guaranteed to make the play-offs.
Unfortunately we've dropped a lot of points at home this season, with the draws against Montpellier and Toulon and the defeat to Toulouse. Those are points we shouldn't have dropped.
"We find ourselves in a position where we have to fight until the end. Whatever happens we will give it our all.
"We've teased each other a little on Twitter [between Italian teammates]. I'm pleased there are Italians in the derby, it shows the country is well-represented in the championship, which is for me the best in Europe."
The game will also mark France hooker Dimitri Szarzewski's final home game for Stade Français before he moves to Racing in the summer.
However Parisse is confident his impending switch to Saturday's opponents will have no impact on the French international.
He added: "Since Dimitri arrived at the club he's always shown his love for Stade Français. He's given a lot to the club.
"He wants to show that if Racing are interested in him, it's because he is a quality player that any team would want to have. As his captain and friend I have faith in him and know he will give his all for the team. There are no worries in that regard."