If you are planning to use your pillowcase on a bed pillow there is really no need to cover the back of the stitching. It will not show as it is inside, against the pillow itself. It could also stiffen the fabric and make it less comfortable to lay your head on.
However, from your photo it looks as though this may be a Christmas holiday pillowcase, perhaps to hold gifts instead of a smaller stocking. Would I be correct?
If so, then you may like to use soft iron-on interfacing across the back of the stitched area to protect it from rubbing, as the gifts are placed inside and pulled out again.