Bath chief executive Bob Calleja believes Stevens has “let down” the club following the 26-year-old’s positive test for a recreational drug.
The prop’s fate is likely to be decided by an independent judicial committee which could convene within weeks.
The matter is being dealt with by European Rugby Cup as the test came after Bath’s Heineken Cup game at Glasgow on December 14.
Stevens, capped 32 times by England, is currently suspended from all rugby and has been removed from the England squad which travels to Portugal next Sunday for training ahead of this season’s RBS 6 Nations Championship.
Stevens could receive a two-year ban, and speculation is rife in the west country that he might have already played his last game for Bath.
He agreed a new four-year deal with Bath last February.
Calleja certainly struggled to contain his anger just four days before Bath’s biggest game of the season.
Victory for Bath in Sunday’s Heineken Cup showdown with French giants Toulouse would see them secure a quarter-final place.
Calleja said: “This week should have been all about the anticipation of a classic winner-takes-all match at The Rec.
“Instead, the headlines have been dominated by Matt Stevens.
“We all feel let down. He has a responsibility, but until all the circumstances are known, I am not going to comment further.
“I know the team remains focused, they realise the importance of Sunday’s game.
“How distracting it will be, we will tell at five o’clock on Sunday. We are going to beat Toulouse.”
Stevens decided to reveal the news himself in an emotional televised interview on Tuesday night, during which he confessed to having developed a problem with drugs.
Calleja would not comment on whether the club knew about Stevens’ intention to go public, merely stating: “It was an interview that was arranged by Matt.”
But Calleja also underlined Bath’s general stance, adding: “This is a very serious matter.
“The club does not, and will not, condone the use of illegal recreational or performance-enhancing drugs by any of its employees.”
Stevens joined Bath in 2002 but is now fighting to salvage his career for club and country, while hopes of touring South Africa – the land of his birth – with the British and Irish Lions later this year appear slim, at best.
Veteran Leicester tight-head prop Julian White has been called into England’s elite squad as a replacement for Stevens.
The 35-year-old returns to the England fold for the first time since making himself unavailable for the 2007 World Cup campaign.