"Ain't too proud to beg" is what the word entreaty is all about. When you make an entreaty, you're begging or pleading for something.
An entreaty is the kind of request you make to King Kong when he's dangling you from the top of the Empire State Building. It's an appeal you make to someone who usually has the power to grant your wish. Entreaty is often used in the plural: "After all my pleas and entreaties, my teacher still gave me a C."