Brown's job looked to be on the line several weeks ago, but City have taken eight points from their last four games and have moved four points clear of the Premier League drop zone.
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"Characters in the changing room have pulled together in their hour of need, in my hour of need and in Hull City's hour of need," Brown told the Hull Daily Mail.
"All of that has resulted in better performances and in better results. You look for men to accept the challenge and they are responding to it.
"It's quite simple, results keep you in the business. There's been an upturn in results and consequently that's why I'm still standing here as a manager.
"I understand that there's pressure and there always will be in any game of football, we all want to win.
"We've all got different agendas, but mine is to make sure I stay as manager of Hull City and we earn a third year in the Premier League."