is it from water hitting the bottom and splashing out, or from a mister misting out the sides or what? just cover the sides and front bottom panel with something and you should be good.
This can be fixed easily! First, spread some newspaper or paper towels around the cage to find out how far away the water dripping goes. Then get some plastic, some door mats, a towel, or even a shower curtain and lay it over the carpet in this area.