Beyonce -- I Don't Fake It ... When It Comes To Crawfish

You're Beyonce and you just faked your way through "The Star-Spangled Banner" in front of millions of people -- including the President -- what's your next move????

CHOWING DOWN ON CRAWFISH AND SWEET POTATO PIE!!!!

After Bey "performed" at the Inauguration Monday, she and Jay-Z jetted down to New Orleans -- and the first thing they did that night ... was hit up the famous Mother's Restaurant.

We're told B and J noshed on some serious comfort food ... crawfish etouffee, potato salad, double grits, french fries, catfish, and calamari ... PLUS sweet potato pie and bread pudding for dessert.

Based on the menu, the meal set 'em back under $100 ... but we're told the two were "very sweet" and tipped "extremely well."