First, I would use a new sharp needle. There are "Universal" needles, but make sure you are using the "Sharps" and I would use the 70/10 size for this type of fabric.
The other thing is to make sure the fabric isn't being stretched while sewn. Even the fabric hanging off the back of the sewing machine could be too much and can cause it to stretch while being sewn. Try to have it as flat as possible going into and out of the feed dogs.
Also, don't be too hard on your self. If you look closely, even the store-bought items made from slippery fabric has puckers.
