No no no...
you got it all wrong.
It's not just the eyes! There are several other things like "hueg eyes with reflections! same face but different hair or different colored eyes! etc..." That create good and beatiful anime-style!
For example Iny-Yasha is prime example of very deep animu/mango style. Every Otaku should always praise series like this one.
For bad example I use One piece. Just look at the picture! That nose! Horrible! That's not like all the other noses in all GOOD LOOKING animes.
Also his face doesn't follow the beatiful shape of "V" chin is supposed to resemble a a triangle flipped up-side down!
Well the eyes are somewhat nice but still... I don't see tons of reflections! Yes! Even when eyes are covered or in shadowed area! And they are not even nearly big enough.
Mouths he tends to make way too dramatic alot of the time. Just remember that mouth is supposed to be extremely tiny when it's closed and covers whole bottom half of the face when open. Chin doesn't move so size of the face always stays the same even though mouth moves.
Oda tends to ignore alot of rules in order to make his drawings more "dramatic" or "comedic" so don't copy him. Oh and if you use animals: always use popular and COOL animals like wolves and tigers. (seriously... Oda used a GIRAFFE in one of his devil fruit powers... NOT. COOL. Stick with cool animals)
And now you know how to draw GOOD manga/anime style drawings. Gambatte! =^___^=