From your description, it sounds like you were trying to use the JPG "quality" slider as a method to reduce the file size.
If I am correct, and that's what you were doing, you need to know that method only works up to a point.
That method only changes the amount by which the image data is compressed. Compress it too much, and it will look horrible. For reasonable quality pix (at any size), one should never set the JPG "quality" (aka, "compression") slider below, say, "6", and for any image that will be examined closely, never below "8" or so.
Instead, what you need to do is change the number of pixels in your image to fit the space on the web page where the image is going. For example, Facebook provides a cheat sheet that tells users exactly how big (...in number of pixels in each direction) each type of image should be:
https://www.facebook.com/PagesSizesDimensions
You need to adjust the pixel dimensions of your image to fit the space FB allows, not by adjusting the JPG quality / compression factor to very low values.
To change the pixel dimensions of your image using PS, go to the "Image" drop down menu and click on "Image Size". Set the units to be pixels, not inches or percent, put a check mark in the "Resample" box, and type in the longer of the two dimensions provided by FB.
Save the result (using "Save As") with a new name so you don't over-write your original file. When prompted, make sure the JPG quality factor is reasonably high.
The above procedure should get you quite close to what you need.
BTW, you may run into a problem if the shape of your image is different from the shape of the space provided on the web page. For example, you have a rectangular image, but the space provided is square. If that is the case, you need to "crop" your image before resizing it. That's a whole other discussion.
Again, let me reiterate that all of the above was based on my assumption that you were using the JPG quality slider as your method of reducing file size. If this isn't the case, let me know.
HTH,
Tom M