I am wondering if the way you saw to do it might have been where you make a template from something like mylar template sheets.
I have done this before - traced the size circle I needed onto the mylar, cut it out, then traced the mylar template onto the fabric. When you cut the fabric, you cut it about 1/4" larger than the template. Do a loose hand basting stitch in the seam allowance you cut on the fabric, and once you get all the way around, place the template inside, and pull the stitching tight. Turn over so the exposed mylar is face down and press. I would use a little spray startch or best press when pressing...remove the mylar template and you should have a perfect circle for appliqueing.
You can also snip a little bit in the seam allowance going right up to just a few threads shy of the line you traced onto the fabric to help your circle turn under better.