You are modeling very low poly but still decide to apply a 1 k texture map? I don't see the use of this workflow, either you make a low poly object ( for games for instance)and apply a small texture map, or as it looks like in this case you want to make something as reall as you can get it, then I would suggest that you bevel the hard edges even it if it is ever so slightly, because nothing in this world has a hard edge like that and it looks very unnatural if you do so. If you really want help post the UV map with and without the image visible this way we can judge where it goes wrong. It looks fairly nice though