Today (March 9) the trust's chief executive, Ron Shields, sat before Hampshire County Council's health and social care select committee to answer the council's concerns.
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Councillors feared that the trust might be spread too thin, with a large geographical area being covered by teams that are short-staffed.
Mr Shields conceded that staffing problems were 'significant' and that this played on the morale of other employees.
Conservative representative for Romsey Rural, Cllr Nick Adams-King, said: 'It's disappointing that the trust has gone down in rating.
'It strikes me that Southern Health is unique in having such a wide range of services - I wonder how sustainable that is when you're facing challenges like this, and if there is a way to concentrate on what's most important.
'Because of where you are, perhaps you have to structure the trust differently.'
Mr Shields responded: 'The overall rating is disappointing, but within that rating the leadership remained good - that says that we understand what the issues are, but aren't making sufficient progress.
'There is a general workforce shortage, with a lack of quality nurses being trained and we're very marginal at times. We can cope, but only until someone calls in sick, or has a family crisis, at which point our staff inevitably feel the pressure.
'It's not just that we're short-staffed, but that staff didn't feel supported for the stress and strain they have been enduring. They have done a phenomenal job and are still delivering top quality care.'
The report paid particular attention to issues at the Beaulieu ward at Western Community Hospital, Southampton, which had not been spotted by the trust's higher ups prior to the CQC's visit.
Vice-chairwoman of the select committee, Cllr Ann Briggs, asked: 'I appreciate there is a lot of good in the report and staff work really hard, but what concerns me is that if the CQC hadn't visited, how would you have picked up these problems?'
Mr Shields said: 'There was a gap between me and the Beaulieu ward.
'In other areas we do see those issues coming through the management process, generally speaking.
'It's a gap that should have been filled.'
Following the CQC's investigation, Southern Health NHS Foundation Trust will be writing a formal response to the health watchdog, as well as drawing up an action plan to fix some of the problems that were raised.