E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To eat humble pie. To come down from a position you have assumed, to be obliged to take a lower, room. Umbles are the heart, liver, and entrails of the deer, the huntsmans perquisites. When the lord and his household dined the venison pasty was served on the daïs, but the umbles were made into a pie for the huntsman and his fellows.
N.B. Pie and patty are both diminutives of pasty. Pasty and patty are limited to venison, veal, and some few other meats; pie is of far wider signification, including fruit, mince, etc.