In the final chapter, "Cry of the Hunters", Jack has lost his authority and Ralph has triumphed. When the naval officer asks, "Who's the boss here?" Ralph loudly replies, "I am."
Jack's actual thoughts are not given, but one can surmise them from what follows Ralph's declaration:
A little boy who wore the remains of an extraordinary black cap on his red hair and who carried the remains of a pair of spectacles at his waist, started forward, then changed his mind and stood still.
Jack probably was experiencing relief, humiliation, and resignation simultaneously. It was all over: life on the island, his role as "king", and the change in his status forever.