Hi,
I have learned the hard way to use some kind of stabilizer even if it is only tissue paper. You will be much happier with the finished product. If you are using a satin stitch on your applique it is essential unless the background fabric is very heavy. One method that solves two problems is to applique your project with the batting already on it. This works well for small projects. THe batting provides stability and the applique stitches do some of the quilting also. You can then put the backing on it later and do only a minimum amount of additional quilting.
Good luck