The 19-year-old USA international arrived late for the game and was left on the bench, before posting the reason on the social networking website Twitter, a move which angered Brown further.
Hull 0-0 Portsmouth: Match report / stats
"It's going to cost him a lot of money, unfortunately," Brown fumed. "That for me is information that stays in house. The reason he wasn't on the bench was our business.
"Jozy was on the bench until 2.10 when I decided to change it. It's unacceptable behaviour, full stop.
"You prepare all week for a matchday, mentally and physically. To ask a player to arrive an hour and a half before a game is not too much to ask is it?"
Meanwhile, Brown played down the absence of midfielder Jimmy Bulalrd, who took a knock in a midweek reserve team outing.
He added: "Jimmy took a whack in the game on Tuesday. It was probably an over-zealous lad who was looking for a scalp.
"He had it on his mind Thursday and Friday and that is the only reason he didn't play any part today. There have been one or two suggestions it's the knee, but the only coincidence is that it's the same leg."
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