Never did that. Is the panel one that you would be comfortable sleeping on or is this purely decorative?

I'll tell you how I would do it. arrange the panel on a pillow case just where you'd want it. Take chalk and a ruler and trace around the panel. Then draw a line 1/4 to !/2 inch in from your tracing towards the center. This will be your fold line, Stay stitch all the way around the square on the fold line. Cut out the center leaving a half inch all around next to the fold line to create a seam allowance. Now clip the corners down to the fold line and on each side of that cut. Press the seam allowance down to the fold line. Now take your panel and pin or baste it in on the wrong side so it shows through the hole you've created. Stitch on the right side close to the fold line--be careful not to catch the other side of the pillowcase. A free arm would be good for this. You can use a decorative stitch or a straight stitch.

If you are making the case too then do this before you sew the case together