Digital photography lenses have far more depth of field than film camera lenses, so it does make it harder to drop the background out of focus in this application. Though using a more telephoto lens will help for this and is the most common choice for small product photography.
If your object is larger than a few inches, like a wine bottle, and you are putting your camera close to the igloo, so the front curtains can be closed, then background information will show up & the current common practice is to remove it in Photoshop & concentrate on the quality of the light on your subject. For larger items like this, most pro photographers will prefer to use soft boxes and reflectors, which give more control. The Igloo was designed to create a simple and easy lighting solution for small products.
A good way to achieve a smooth background without working in photoshop is to use paper. Commercial product photographers (primarily in the days before photoshop) had a roll of paper in a variety of colors and sizes. If you get a piece of thick construction paper (art supply store) & attach a few strips of sticky back Velcro to in the same location as the cloth included with your LiteIgloo, that may be your best solution.
Check out the equipment lessons tab of the http://www.photoflex.com/pls for Lessons using the LiteIgloo