The mat you purchased is intended for hard floors only. It has a smooth bottom to accommodate hard floors like wood, tile, vinyl, etc. Based on your review, it sounds like you purchased the wrong style of mat for your flooring surface.
You likely should have purchased a carpet mat, which has cleats on the bottom to keep the mat in place on carpets. These cleats work as a gripper and won't allow the mat to move or slide. Carpet mats are available on homedepot.com.