Hull are 19th in the Barclays Premier League with just four points from seven games but their dismal run stretches back to last December, since when they have won just twice in the competition.
"I think I have got a good support mechanism in terms of management staff and in terms of the chairman and the owners," said Brown. "As far as I am concerned, until they say different, no I am not fighting for my job."
He added: "As far as I am concerned there is a lot more to achieve at this football club."
Last week's 6-1 thrashing at Liverpool turned up the heat on Brown and he now faces a crucial month with games against Fulham, Portsmouth and Burnley following Wigan's visit to the KC Stadium.
Brown said: "A lot has been made of the month, a lot made of the six games coming up.
"But of the six coming up, they mean nothing unless you win the first one.
"We are not getting away from the first game - we are not looking further than Wigan. It is an important game for us.
"We are looking at going into the international break by getting something from this game, and carrying that into the remaining games in October."