A new independent review into 10 killings has revealed the extent of the failings at the Sussex Partnership NHS Foundation Trust.
The trust has already apologised for its role in the lead up to the death of Donald Lock, who was stabbed 39 times on the A24 in Findon in July 2015. But the new review has found the trust did not always learn fully from previous mistakes and sometimes "severely underestimated" the risk posed by mental health patients.
It also found that the trust failed to include the views of families, some of whom pleaded for help, and did not always send people with signs of psychosis to specialist services.
Commissioned by the trust and NHS England, the review analysed previous reports into the 10 killings to see if any lessons could be learned.
In two cases, experts concluded the deaths could have been prevented - although it did not say which ones. Neither of them was the case involving Donald Lock.
Lock, who was 79, was killed by Matthew Daley following a collision between their cars. Daley admitted to the stabbing, claiming diminished responsibility, and was convicted of manslaughter in May. The court heard that Daley suffered from chronic mental health problems and that his family had pleaded with the NHS to have him sectioned.
Sussex Partnership has admitted it "got things wrong" and should have carried out a formal assessment for Daley, who had a diagnosis of Asperger's - but who was also suffering from symptoms of psychosis.
Lock's family has said they believe the NHS trust is to blame, saying he would "still be here today" if it had done its job properly.
In the new review, investigators found that in seven of the killings, there was criticism of how the NHS trust assessed the risk posed by its patients.
Investigators found that assessments were not updated when circumstances changed - such as a new criminal conviction - while some assessments were started but not completed.
The report said learning after each killing was not always taken up across the trust and there was some "repetition" in the recommendations made after each one.
Colm Donaghy, chief executive of Sussex Partnership, offered his "sincere apology and condolences" to the families.
He added: "We commissioned this review with NHS England because we want to make sure we have done everything possible in response to these tragic incidents."