The Aviva Premiership club announced on Wednesday that rugby director Sir Ian McGeechan will leave at the end of this season, while it is thought forwards coach Martin Haag will not be offered a new contract.
Bath currently lie eighth in the Premiership with just three games left, meaning they face a fight to secure qualification for next season's Heineken Cup.
Bath say they are making "good progress" in identifying a head coach. Press Association Sport understands South African Gary Gold and Australian Michael Cheika are the top two contenders.
And multi-millionaire Craig has now written an open letter, published on the club's website on Thursday, offering his thoughts on what has been a poor campaign.
"I would like to take this opportunity to address everyone concerned with the performance of Bath Rugby," he said.
"I am the first to admit that this season has been disappointing and frustrating. We have been inconsistent and have under-performed.
"A considerable amount of time and money has been invested in the club this year without the returns expected by everyone.
"It hurts to be in this position, and all of us involved with the club understand that the overall performance has not been acceptable. We know we could, and should, have done much better.
"What I can say is that some hard lessons have been learnt, but our objectives and vision have not changed and we will continue to build the solid foundations for long-term success.
"Rugby is an important part of Bath, and striving to be champions is our goal.
"I still believe the squad is as competitive as any in the Premiership, and with a few new signings arriving over the summer and the fact the players will have been together for much longer, there is real reason to look forward positively."
Craig then addressed the coaching situation, confirming a new head coach and structure would be announced in the coming weeks.
"Focus will be placed on strengthening some of the areas of our game that have been weak this season," he added.
"And our aim will be to concentrate on producing hard, attacking rugby with a style of play that our supporters associate with Bath Rugby.
"All of us at Bath Rugby appreciate the faithful support that follows the club and know how much playing success means to each one of our supporters.
"I am committed to ensuring we do everything possible to enable that long-term success, supporting the players and coaches to be able to deliver.
"There are no hiding places in top-level sport, and I am still very confident that with more hard work this club and its players have the ability to perform at a level that will meet all our expectations."
Gold is currently in temporary charge of Premiership relegation favourites Newcastle, while Cheika is at French club Stade Francais.
Gold took the reins in January, charged with trying to keep Newcastle in English rugby's top-flight, but they are currently eight points adrift at the basement with just three league games left.
Former Harlequins supremo Dean Richards, whose three-year worldwide coaching ban imposed following his role in the 2009 Bloodgate saga expires this summer, has already been appointed as Falcons rugby director next term.
Gold has previous Premiership experience with London Irish, and he arrived at Kingston Park after being part of South Africa's coaching staff during the World Cup in New Zealand last autumn.
Cheika, meanwhile, led Leinster to European title glory in 2009, and he went close to European success with Stade last season before they suffered an agonising Amlin Challenge Cup final defeat against Harlequins.
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