bad / badly
The adjective after a linking verb versus the adverb after an ordinary verb.
After a linking verb, use bad: I feel bad, it looks bad. After an ordinary verb, use badly: He played badly. When feel is a linking verb, use feel bad.
Examples
Use I feel bad about the mistake. (linking verb; adjective)
Use The cut looks bad. (linking verb; adjective)
Use He slept badly. (ordinary verb; adverb)
Avoid I feel badly about the mistake. (linking verb; needs the adjective bad)
See also adjective / adverb after linking verbs.