So I made this. With no pattern. This is all you have to do:
1. Measure your mat's length and circumference. Add 3 inches to both measurements. Example: My mat's circumference is 13 inches and is 24 inches long. My fabric measurements are 16" by 27". I just used a piece of scrap fabric from another project.
2. Cut a strip (matching or not) about 3" by 27" (the same length as your first piece). If you want a wider strap, go with 4" by 27".
3. Cut 2 circles using an object in your house that has the same circumference as your mat + 4" (so mine is 17"). I used a tray for a bunch of blank DVDs. Keep the circles together with right-sides out. Baste if you want. I hate basting and pinning so I usually don't.
4. Sew the strip, right-sides in, length-wise. Sew one end of the strip closed. Turn right-side out.
5. Sew the main piece of fabric, right-sides in, up the side.
6. Sew the circle pieces to the bottom of your main piece (circles are still right-sides out and back to back, main piece is still right-sides in). I didn't pin mine, I just held the edges as I went. It's easier if you keep the circle piece on bottom and your main piece on top as you go around the edges so you can use circle as a guide.
7. Hem upper edge of case. You can either add a drawstring here or add a snap or button for closure. Or leave it open. Totally up to you!
8. Turn your work right-side out. You're almost done!
9. Attach the strap about 3" from bottom and top (tuck the edges in on the open end of the strap before sewing to leave a clean edge).
Namaste