A predicative Complement is a Complement of a verb that describes the Subject or Object of that verb.
- Bob is a doctor.
- Bob is happy.
In the sentences above, the phrases a doctor and happy are Predicative Complements, because they describe the Subject, Bob.
The verb FEEL also takes Predicative Complements:
- I feel hot.
- I feel an idiot.
Adverbs cannot function as Predicative Complements:
- *He is happily. (ungrammatical)
- *I feel hotly. (ungrammatical)
The verb feel usually takes adjectives as Predicative Complements.
The Original Poster's example
I feel loved.
The word loved cannot be an adverb in the Original Poster's example because it is appearing as a Predicative Complement of the verb FEEL. It looks quite a lot like a verb. However, we can show that it is not a verb in the following sentence where we use the word very to modify it. We cannot use very with verbs:
- I feel very loved.
- *I very love you. (ungrammatical)
The word loved is an adjective here.
However, loved could be a verb in this sentence where it appears with a by preposition phrase:
- I feel loved by my parents.
The word loved could be either a verb or an adjective in the Original example.