yeah the type of dithering you used is really just an old technique for making colors of devices with a limited color amount (think of an old motorola phone or something). It really doesn't look good on a large device like i monitor. Most practical applications of dithering in pixelart nowadays is to show some texture and it's usually used in very small amounts.
good examples of using dithering for texture
a good example of using dithering to create another tone on a limited palette
good examples of using dithering for texture
a good example of using dithering to create another tone on a limited palette