I'll give you doubters some things to ponder:
The majority of the energy required for space flight is overcoming gravity and air friction. After you escape the atmosphere, the energy required to maintain flight drops off rapidly.
The space shuttle is capable of reaching high Earth orbit.
The difference in energy required to travel to the moon and back from high Earth orbit is almost nil when compared to the energy required to reach orbit in the first place.
The space shuttle, when compared to the earlier space vehicles is a flying brick. A very heavy flying brick.
Earlier rockets actually had more fuel capacity than the space shuttle.
Basically, early rockets = '67 427 Vette. Shuttle = GMC 3500. If the shuttle can almost escape Earth's orbit...