The Dons sit ninth in the table and have picked up just one victory in their last nine outings in all competitions.
They face a tough challenge when Motherwell come calling on Saturday - a side the Dons have failed to defeat in the league since 2008.
But veteran boss Brown refused to be downbeat about forthcoming matches, while claiming he is not feeling the pressure.
He said: "You've got an accountability to everyone here at the football club - the chairman, the board, the fans. You've got that in every game. I want the best for Aberdeen Football Club, that's my job. I'm certainly accountable.
"But I don't feel pressure. I'm not losing sleep. I'm conscious of the fact that we want to do as well as we can. I think the fair-minded people will look and say that we've had some misfortune but we've had some poor performances.
"Not all that many, I would have to say, but the last game was one of them and we must get that out of our system. I'm not contemplating not being in the top six. I'm optimistic about it and we're focused on getting there."
Asked if James McFadden - back at Motherwell for a second spell - will be the one to watch at Pittodrie, Brown said: "He's one of many. The Motherwell team are confirming they are the second best team in the country.
"We've put them out of the cup in the last two seasons away from home and the last two games we've played here have been draws.
"So we just need to try to edge a step further. I think they are respectful of our team and we are certainly respectful of theirs."