I think what goes around the grass tile is very important to consider. Look at Link to the Past, the grass is just a solid color with a few grass blades here and there, but it looks ok because of the other tiles around it. No matter how good your grass tile is, it will look boring if the majority of the screen is filled with just it. You need to think about composing the screen. I would start by roughly sketching a screen for your game at your intended resolution. Keep tiles in mind, but dont worry too much about the grid or tileability. This will help you figure out what style of grass will work with everything else around it to make the whole screen look right. Making each texture as an isolated object, I think, is the wrong way to go about it.
I agree and too many people make the same mistake IMO.
Try sketching out a mockup scene in your desired resolution.
Don't get lost in details, start out with blocks of colour keep working around the scene so you keep a consistent style.
Check out this amazing work in Seyken: Crystal Kingdom below.
Notice how the grass is smooth except where some blades of grass pop up.
Notice the patches of variation.
And all done with just a few colours in the ramp!
This obviously requires a high level of skill so don't cry if yours doesn't look that good (like I do!
), hopefully you get something out of it though.
If you want to improve, its best not to emulate any style in particular but its always good to learn what you can and move on.