Your body expels fiber for a good reason. It is used mostly to clean out your digestive tract, which is very important. It's not meant to be retained.
Juicing is actually perfectly fine. When you eat a whole carrot, yes there is important fiber, but the vitamins are less bioavailable than with fresh carrot juice.
My advice obviously is to do both, not just juicing. If you are going to juice, make sure you also eat enough fiber from either fruits or vegetables, or other grain sources.