Here's why:
* "Bad" is an adjective, describing a state of being.
* "Badly" is an adverb, describing how an action is performed.
In the phrase "to feel bad," you're describing a feeling or emotional state. Therefore, you need an adjective to modify the noun "feel."
Example:
* Correct: I feel bad about missing your birthday party.
* Incorrect: I feel badly about missing your birthday party.
Let me know if you have any other grammar questions!