*Nevertheless, human feelings are quite complex than of animals.
The sentence above is not quite grammatical. First of all, the than-phrase that we see here cannot be used freely with any old sentence. These than-phrases usually depend on a comparative form of adjective or adverb earlier in the sentence. In other words, the comparative adjective or adverb licenses the existence of the than-phrase. So if we change quite complex to more complex, this should make the than-phrase acceptable:
- Human feelings are more complex than ....
However, there is another problem with the Original Poster's example. This is that, following the word than, we need a phrase which parallels the main clause in some way. We can delete any bits that can be recovered from the main clause, but it must be clear how the deleted material fits in to the proposition after the word than. But there is nothing that we can clearly reconstruct here. We need something like:
- Human feelings are more complex than [animal feelings are complex].
We could delete different bits from the second clause here:
- Human feelings are more complex than [animal feelings are
- Human feelings are more complex than [animal feelings
We could replace feelings with a pro-word one
- Human feelings are more complex than [animal ones
But we cannot replace that last sentence with a preposition phrase, because it isn't clear where this preposition phrase fits in:
- *Human feelings are more complex than [ of animals
The problem is that the phrase of animals needs a head word in the noun phrase - otherwise it is not clear what it is modifying or replacing in the subordinate clause. If we use the word those, this should do the job. Those will be understood as referring to feelings, mentioned earlier on:
- Human feelings are more complex than [those of animals
Without the distracting brackets, this gives us
Human feelings are more complex than those of animals.
The preposition of works quite nicely here.