Speaking publicly for the first time about the 14 charges brought against Vincent and six against Arif by the England and Wales Cricket Board, the county expressed their distress at the allegations.
Sussex's players and coaching staff met on Sunday to discuss the charges relating to two matches in August 2011.
Captain Ed Joyce spoke of the anger felt in the changing room, but the strongest words were delivered by Robinson.
"Obviously the last couple of weeks has been upsetting for everybody connected with the club and especially for the players and coaches involved in that period," Robinson said.
"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 than 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.
"My reaction to these stories was anger. There was a lot of anger in the dressing room," Joyce said.
"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."
- Sports & Recreation
- Ed Joyce