Backstitch using some thread and a sewing needle! I chose purple thread as it matches my headphones

I'm no sewing expert so I'd personally suggest looking at some online tutorial images to show you how to get the nice backstitch.

If your needle at any point snags onto some white elastic on the inside of the band, carefully try and unsnag it and try to put the needle back through without moving it again. You might find giving the band a stretch helps putting it back.

As you can see the backside doesn't need to be neat..