Other mistake: Just after Grandma Willow says "There's still some snap in these old vines," John Smith puts on his bag, but he just presses it to him instead of putting it over his head.
Other mistake: When Percy sees Meeko in the bubble, it is done in first person perspective and we can see straight through the bubble, showing that Meeko is not there on the other side.
Answer: He probably knows that if he tries to escape he'll be shot down by the Powahatans' arrows. He prefers dying with some kind of dignity rather than while running.