How to Store Fresh Pasta: If you’re not cooking the pasta right away, cover your well-floured spinach pasta and place it on a tray covered with plastic wrap. Leave at room temperature if cooking within 1-2 hours. Alternatively, refrigerate until ready to cook, up to 12 hrs. It’s best to cook homemade pasta on the same day it’s made, otherwise it might oxidize, discolor and stick together if chilled past 24 hrs.