Rest assured! Something can be done about that!
Here's to go about it: start by using a width of your image that is 2048, 960 or 720. To check or change your image size go to Image > Image size
Second thing to check is if your image is in the RGB Color. Check or set in in RGB Color using Image > Mode > RGB Color
After you've checked all that, save your file: go to File > Export > Save for web. A new screen appears.
Choose JPEG on this screen and a quality of around 97. Be sure to tick the checkbox 'Convert to SRGB'. Check if the width of your file is correct and hit the save button.
There you have it! Now your image has the same awesome qualities on Facebook as it has in Photoshop!