David Morton-Holmes, 55, died as a result of alteplase being given to him, a drug used in thrombolysis treatment.
The family was represented by law firm Hugh James at the inquest on May 17.
The firm said it is now recognised Mr Morton-Holmes did not meet any of the criteria for administering alteplase but, despite this, he was given it, and without the close monitoring it requires.
Mr Morton-Holmes was taken to the Conquest on February 4, 2019, after flying home from holiday the previous day.
His blood pressure was raised and he had numbness in his left arm.
A head CT scan was arranged and a decision was made to administer alteplase, an anti-coagulant that affects blood clotting.
Hugh James solicitors said Mr Morton-Holmes deteriorated shortly after it was administered and a repeat CT scan showed numerous areas of bleeding in his brain. He was then transferred to Eastbourne DGH but died on February 8, 2019.
The trust has since apologised to Mr Morton-Holmes’ family and said it will ‘learn lessons’ from the case.
It admitted that there were no specialist staff at the Conquest Hospital as stroke services are based at Eastbourne Hospital.
Mr Morton-Holmes’ family also criticised the trust for taking three years to publicly acknowledge the care it provided to him was wrong.
Lynda Reynolds, represented the family as solicitor. She said: “This has been a case where it was clear that there had been a tragic failure in the care provided to Mr Morton-Holmes. Instead of recognising the errors, which were highlighted in internal emails the trust decided to attempt to stand by an investigation that was not credible.
"The family have been treated appallingly by the trust with no recognition of their continued distress in failing to address the fundamental failures that led to Mr Morton-Holmes’ death.
“The request to postpone the inquest in October 2021 after knowing that the investigation was inadequate from at least November 2019 was inexcusable. “The family had already lived in the knowledge they would have to attend the inquest for two-and-a-half years to then have it postponed caused huge distress.
“It is now more than three years since Mr Morton-Holmes’ death and they have only just concluded the inquest.
“I understand that errors occur, and in themselves these were very serious errors in judgment and failing to follow all the relevant protocols, but to add to this the apparent disregard for the family in the time following Mr Morton-Holmes’ death requires an explanation at the highest level.
“The family want to ensure that their loss is recognised and that lessons have been learned.”
An East Sussex Healthcare NHS Trust spokesperson said: “We want to express our deepest condolences to the family of Mr Morton-Holmes and apologise for the failures in his care. The treatment provided to Mr Morton-Holmes fell below the standard that he was entitled to receive.
“We will look closely at the coroner’s findings alongside our own investigations to learn lessons from this case to ensure that nothing like this happens again.”