I germinated some by accident in a balled up paper towel left in a brief rain. I realized what happened but the seeds were very tiny so I couldn't figure how to move them and where to move them. In a pinch, could you just set the towel on soil and sprinkle a bit of soil on them, leaving the paper towel to rot away? Keeping them misted?
In a pinch, it is better to keep them on the paper towel than to break the fragile first root. Quality paper towels hold up really well which is unfortunate in this case. Consider cutting the towel and placing each sprout in it's own container so the roots don't need to be jostled again. Cover the root with soil but leave cotyledons above ground if they are open. (Those are the first set of leaves.) Since I don't know what you are trying to grow, I will leave it at that. Good luck