Using black yarn, embroider nose in satin stitch and make two French knots for eyes.
From the guardian.co.uk
Stitches like the herring bone stitch, satin stitch, back stitch and cross stitch are occasionally used.
From the en.wikipedia.org
Since felt won't fray, it's not necessary to cover the edge, but a satin stitch gives a more professional look.
From the tennessean.com
Satin stitch, all around, overlapping the edge.
From the en.wikipedia.org
Use a straight stitch to place the shapes, then sew a second time with a very closed together zigzag or satin stitch to prevent the raw edges from fraying.
From the nzherald.co.nz
Since satin has a tendency to pucker, try different stitch lengths, maybe different threads.