Is it normal for new tattoo ink to come off?

I got a new tattoo on my lower back last night, its al black and a pretty decent size. I tried as hard as I could to sleep on my stomach but must have turned over while I was sleeping. There is little black smudges on the sheets and when I washed it this morning a little more ink showed up on the towel. my tattoo looks okay but I REALLY dont want to have to go get it touched up so I was just wondering if this is normal...?