You have to overwrite the keyDown function in Stage.
See this example code
mStage = new Stage() {
@Override
public boolean keyDown(int keyCode) {
if (keyCode == Keys.BACK) {
Gdx.app.exit();
}
return super.keyDown(keyCode);
}
};
Gdx.input.setInputProcessor(mStage);
Gdx.input.setCatchBackKey(true);