Atticus is a very unique person. He is a man of integrity and drive. He cares about people. When the verdict was read, he would have felt both resignation and sadness.
Atticus knew that there was no way the jury would acquit. Even though he proved that Tom was innocent, it would not matter. There was no way the jury would take a black man’s word over that of a white woman. He would have felt resigned to the fact that the jury would convict, meaning he expected it and was prepared for it.
When Scout asks Atticus if he is going to win, long before the trial actually starts, he tells her no.
"Simply because we were licked a hundred years before we started is no reason for us not to try to win," Atticus said. (ch 9, p. 54)
Atticus is basically telling her that history and society is against them, but they have to try anyway. They have to try for Tom’s sake.
Atticus is sad, because he does care about Tom. He is willing to appeal, and has told Tom this. He knows that the appeal is a long shot as well, and Tom’s conviction is unlikely to be reversed. However, he thinks he has a better chance than in the local court.
"Before I'm through, I intend to jar the jury a bit- I think we'll have a reasonable chance on appeal, though…” (ch 9, p. 63)
Atticus tries his best for his client, and a lawyer never likes to lose a case. But Atticus is not naïve. He knows that the guilty verdict is a forgone conclusion. He does what he can anyway.