Generally, when your back does not like lying flat to the floor, it is because you have an over-flexible lumbar. When you come into Savasana, recline back with your knees bent, lift your buttocks slightly off the mat and use your hands to lengthen the sacral flesh towards the back of the thighs before placing your pelvis back onto the floor. Then straighten your legs with resistance. If this doesn't relieve the discomfort, (and if your lower back is spasming, I doubt that this will be enough of an adjustment,) then place a bolster or some high cushions under the backs of the knees or maybe even better, rest the lower legs onto the seat of a chair. As time goes by, and your back muscles become longer and stronger, the spasming will reduce. You do need a trouble free Savasana at the end of a practice though. It is vital to sooth the nervous system.