Is this head band machine knit

http://images-ff.asos-media.com/shmotterstorage/4276/large_c0bd09a2-dc0e-4770-a351-2f30080e328f.png

I tried to knit but my stockinette looks “handmade” compared to this one which looks like it was knit by a machine.

Yes, it’s definitely machine knit with very thin yarn and very small ‘needles’. If you want to replicate it, you’d need laceweight yarn and maybe size 1 or 2 needles, with a lot of stitches. You could use sock yarn and size 3 or 4 and remember knitting looks better after it’s washed to even out the sts.