Do the finished circle. Measure the circumference of the pot knob with the elastic in it's original shape and mark. Cut the elastic a little past the mark for overlapping. Use the #4 stitch to sew the elastic to the inside of the circle and you're done. The #4 on my Bernina is the one that looks like a zig zag but with little stitches. The first one would be a trial until you can get the right spot to sew the elastic onto a circle. To sew elastic that gathers, you anchor the first and the stretch the elastic as you sew until you can overlap the 2 ends a bit.
It looks nice but I have a few cotton crochet dishclothes that I use in the same way. I put one over the know of my corningware and snap on a broccoli elastic. Easy Peasy!