Though possessed of enormous courage, Atticus is only human, after all. And, like most people would be if they were faced with a baying, angry mob, he's understandably frightened. But it's not in Atticus's nature to make a big show of things; he's always been very restrained in displaying his emotions. Besides, he has to stay strong for Scout's sake. He can't let her see her father showing visible fear in the face of such real and present danger. That's why he tries to act as normally as he can under the circumstances, meticulously creasing his newspaper and rising from his chair slowly, like an old man. And it's also why he puts his face to the jailhouse wall as he wipes the worried beads of sweat, and perhaps one or two tears of blessed relief now that are gone, from his face.

Atticus does his best not to show his fear.  He deliberately and slowly creases the newspaper.  He talks slowly, moves slowly, and his voice doesn't change.  When Scout shows up, he shoots her an angonized glance. Scout says "A flash of plain fear was going out of his eyes..." (pg 154) When the men confront him,  Atticus puts the newspaper down "very carefully" and then Scout notices that his fingers were trembling a little. When the men leave, Atticus goes to the jailhouse wall and leans against it with his face to the wall. He takes out a handkerchief and wipes his face and blows his nose violently.  One can infer that he shed a few tears. All of these actions indicate that Atticus was frightened.  He was one person facing a mob, and his children were in the middle of it.