If in doubt, always call your vet or the Animal Poison Line immediately.
A sudden high-fat meal is one of the most common triggers for pancreatitis in dogs. The pancreas becomes inflamed and in severe cases this can be life-threatening. Avoid giving fatty trimmings, roast skin, gravy, or any high-fat table scraps.
If pancreatitis is suspected, contact your vet : it can require hospitalisation. A bland diet (plain rice and chicken) may help mild cases.