The England and Wales Cricket Board last Thursday charged Vincent and his former Sussex team-mate Arif of Pakistan with fixing the outcome of a 40-over county match between Sussex and Kent in August 2011.
Former New Zealand cricketer Vincent is also accused of fixing a Twenty20 match between Sussex and Lancashire in the same month.
Sussex's players and coaching staff met on Sunday to discuss the charges relating to those two matches.
Captain Ed Joyce spoke of the anger felt in the changing room, but the strongest words were delivered by Robinson.
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"The stories we've read have caused a lot of distress. We're all deeply shocked.
"The players' ethos is based on a will to win with a togetherness that means everybody has to drive towards achieving the same goals.
"The thought that anybody among us, at any time, may have been working against that aim sickens and disgusts us."
Robinson's view was echoed by Joyce, who understands that perceptions of Sussex could be tainted by the actions of Vincent and Arif.
"The question 'does Sussex have a problem?' is what comes when you get a couple of alleged bad apples in your team. People start questioning the things you do.
"We met on Sunday morning and there was a huge amount of anger there because everything we do as a team is about winning games.
"To think there could be people in your midst who aren't doing everything they can to win is the worst thing you can do to a professional sports team."