A team of 60 inspectors visited the hospital in December and January and found improvements were needed in providing safe and responsive care.
However, the report also found the trust provided services that were caring, effective and well led.
The chief executive of the trust said progress was being made by staff.
Fiona Dalton said: "We all have a lot to be proud of, but there is much we still need to do to reach our ultimate aim of ensuring every patient receives perfect care and treatment with us.
"We know there is a long way to go, but we are making progress and, with the brilliant individuals and teams we have in place across the organisation, it is something we know is achievable."
In September last year the parents of five-year-old patient Ashya King removed him from Southampton General Hospital.
In response to that, the CQC report said: "The trust had independently reviewed its procedures, and had cooperated with others across health and social care, including the Local Child Safeguarding Board, to review the incident.
"The safeguarding actions taken were deemed appropriate, but there were areas for improvement."
The trust provides services at Southampton General Hospital, the Princess Anne Hospital and Countess Mountbatten House, and outpatient services at the Royal South Hants Hospital.
The Care Quality Commission has rated University Hospital Southampton NHS Foundation Trust as requiring improvement following an inspection.