Jem may be a young boy, but he is mature and intelligent enough to recognize that Tom Robinson is an innocent man, and that the jury deliberately disregarded the evidence presented and convicted him anyway. Jem no longer trusts the good people of Maycomb, who he considered
"... the best folks in the world, least that's what they seemed like." (Chapter 22)
He wonders if Tom or Atticus have any real friends or supporters in Maycomb, and his new "fatalistic" view includes the realization that
"... can't any Christian judges an' lawyers make up for heathen juries... Soon's I get grown..." (Chapter 22)
Miss Maudie's positive reinforcement doesn't seem to have any effect on Jem, but it becomes obvious that Jem is looking to the future. When he is grown, he speculates, he will be able to make a difference--either as a lawyer, like Atticus, or as an honest juror who lives up to the court's expectations of making a fair, unbiased decision.
Immediately following the Tom Robinson verdict, Jem breaks into tears. Jem continually repeats the phrase "it ain't right" after he witnesses Tom become a victim of racial injustice. Jem has suddenly lost his childhood innocence and becomes jaded toward the prejudiced members of his community. When Miss Maudie invites the children over to eat cake, Jem wears his emotions on his sleeve and mentions that for his whole life he had naively believed that Maycomb was the safest place in the world. Miss Maudie then attempts to ease his feelings by explaining that there were multiple people who tried to help Tom Robinson. However, Jem is not comforted by Miss Maudie's kind words and continues to reflect on the prejudiced community of Maycomb. Jem then says, "Soon's I get grown." Jem's final statement implies that he is already thinking about changing the judicial system in Maycomb when he becomes an adult. Jem's traumatic experience drastically changes his perspective on his neighbors and gives him an incentive to make a change as an adult.
I think Jem's new perspective was that he complains that his illusions about Maycomb have been shattered: he thought that these people were the best in the world, but, having seen the trial, he doesn’t think so anymore.