GIF pixels can only be 100% or 0%. Transparent or opaque. They cannot be dithered or have gradient opacity.
You need to set the matte color as whatever background you're creating the GIF for. For example, I made this using 3DS Max, and created the GIF in photoshop:
Seems transparent and smooth, yeah?
But if you drag the image to a new tab, where the background is just white, you'll see that while the blue color still matches the sythe background, it's not truly transparent.
Here's those settings:
Notice the Matte color. It's set to #0F1C2B, which is sythe's background color.
Crisp images like that pikachu will come out well enough because the edges are so hard. The white default matte around the edges is hardly noticeable, but once you get into anything with soft edges, glows, shadows, etc., you'll have to consider matching matte to your intended background color.