How to Use Applesauce in Baking...Or, How NOT to....

Since I am still learning how to bake, and alter recipes, I have a question for any readers out there...

I have yet to figure out how to perfectly substitute applesauce for butter and/or oils. I attempted to make my Whole Wheat Carrot Cake Oatmeal Raisin Cookies last night with this method and you can basically stamp a big FAIL on that. They turned out nasty, ugh.

I know that doing this can in turn make your finished product dry, but is there are way to use applesauce that keeps a somewhat similar flavor and texture to the original?