Brown revealed his displeasure immediately after the game – even joking that he hoped Geovanni failed a post-match drugs test for which he had been singled out.
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As it turned out, the doping control gave the former Barcelona player a chance to regain his cool and then say sorry for his behaviour.
Brown welcomed Geovanni's contrition but has told his creative lynchpin that with Hull now very much in a fight for top-flight survival, there is no room in his team for hot-heads.
"He was very apologetic for his actions," Brown said. "But as far as I was concerned his actions were those of an angry man, as opposed to a composed man, and that's what I'm looking for.
"I'm looking for players who go across the white line and compose themselves, and can respect the decision (to substitute him) for the reasons it was taken.
"It was taken for the right reasons. If I printed the stats it would be there for everybody to see. But I'm not going to wash dirty clothes in public."
Reports have suggested Geovanni was fined by Brown for his fit of pique, but the City manager denies that is the case and insists he will be considered for tonight's crucial trip to face Fulham at Craven Cottage.
The 29-year-old was taken off as part of a double substitution just eight minutes into the second half on Sunday, following a largely ineffectual display which was typical of his recent dip in form.
Brown believes the Brazilian may be suffering from nerves as the season enters its most crucial phase.
Meanwhile, Fulham manager Roy Hodgson has started to dream of Europe now the Cottagers have begun to establish themselves as a top-10 outfit.
A side that avoided relegation by the slenderest of margins last season are currently ninth in the Premier League table and go into Wednesday night's game just three points behind seventh-placed West Ham.
Hodgson said: "The Uefa competitions are something that mean a lot to me personally so it would be very nice if I could take part again with Fulham."
Hull will be without ex-Fulham midfielder Jimmy Bullard, who suffered a serious knee injury just days after leaving Craven Cottage in January in a £5million deal.
The England squad man had been disappointed that Fulham had not been willing to grant him the contract extension he craved and was quick to sign on the dotted line for Hull once a four-and-a-half-year deal was offered.
But Hodgson insisted: "There is no ill feeling whatsoever."
Defender John Pantsil returns from suspension to replace the injured Chris Baird at right-back.