The pilot was landing the tailwheel-equipped airplane at the conclusion of a cross-country flight. He stated to a Federal Aviation Administration (FAA) inspector that he applied left brake during the landing roll and the airplane veered off the left side of the runway and traveled down an embankment, resulting in substantial damage to the right wing and right elevator. The pilot stated that there were no mechanical malfunctions or anomalies that would have precluded normal operation of the airplane.