When resizing a design, my images become extremely pixelated. The image size required is very small (192 x 48 pixels), and my assets are much larger. I've tried resizing the assets themselves but they become pixelated when I do that as well. I'm sure I'm missing an easy fix - Any suggestions?
You're not missing anything. That's just how it works and at such a small size you're basically talking good old pixel-by-pixel optimization like it used to be necessary for icons or game sprites. Anything more than this statement of fact will require a specific explanation of what you want to achieve/ need to do for what purpose and what sources your work is based on.
The image part of your screenshot measures 1152 x 288 pixels, which means that you're viewing the image at 600% view. Any image will be pixelated at that magnification.
To see a true representation of the image, view it at 100%, where one image pixel is represented by one screen pixel.