I thought of a different way to attach the felt to the Tyvek:

sewing them together so the felt would be seen in the outside.

The problem is that in this way there is no place for mistakes: everything is seen. And since I don't cut so good it's pretty much a challenge for me..

To secure the stitches I sewed once a normal straight stitch and one zigzag.

I took it to Despina's class and showed it there. The reactions were positive, but after I passed it in class it got torn. So I need to secure the stitches better.