From a military standpoint, the result is a victory for the Union troops. Although Henry ran from battle, most of the troops held and repulsed both the first and second attacks by the Confederates. That's why Henry is so embarrassed. If his unit had lost the battle, more might have run or the entire unit might have been forced to retreat. Then he could possibly justify his actions. However, a victory meant that he had faced his battle with courage and lost. He had run away from battle when there had been no need.
From a military view, the Union soldiers managed to hold off the Confederates. Henry ran from the battle, but a sufficient amount of soldiers held their positions. The soldiers that remained were able to repel the opposing forces, and so ensured a victory for the Union. Henry is very embarassed about running from the battle, and also scared that he will be branded as a deserter, and so tries to hide the fact that he was absent when the battle took place. From an overall military standpoint though, the Union forces won.