Simon Smith, 51, went to the hospital in July 2018 after suffering severe pain in his leg. He was eventually diagnosed with a rare infection in the thigh bone, which triggered sepsis - an infection.
Dudley Group NHS Foundation Trust's medical director Julian Hobbs told Mr Smith's inquest that changes to working practices were underway at the trauma orthopaedic department at the time of the incident and that more staff had been appointed since then.
Giving evidence on Friday at the hearing held in Oldbury Mr Hobbs said: I have spoken to the family on a number of occasions. We absolute recognise omission of care that Mr Smith had. It is not the standard of care that we would aspire to.
"We have improved enormously and continue to do so. Our improvement is not complete and it is something that the orthopaedic team is relentlessly pursuing and we are very sorry."
Mr Smith, of Bullfinch Close, Russells Hall, Dudley, had begun to show signs of sepsis, including a high temperature and raised heart rate. But the inquest heard that trauma orthopaedic staff failed to give him antibiotics at an early stage to treat the condition until days later and he went into multi-organ failure.
Giving evidence, orthopaedic consultant Dr Donal O'Donoghue, who carried out an independent review of Mr Smith's case notes, said: "This delay was in my opinion was both avoidable and later led to Mr Smith's death three months later."
He told the hearing that a "gold standard" investigation to find the cause of the patient's pain would have been an MRI scan and if that wasn't available then an alternative scan.
"There was a lack in appropriate degree of urgency. The records do not make it clear that there was a diagnosis of sepsis when in contact with Mr Smith," Mr O'Donoghue said.
He added: "This delay to my mind was inexplicable and inappropriate. There is no explanation given."
The inquest previously heard from the trust’s consultant trauma orthopaedic surgeon, Mr Qutub Qadri that it had been a busy time and he was acting on limited information provided by junior colleagues, that he had requested the MRI scan and was not aware until two days later that it was broken. He also said he was not told about a spike in Mr Smith's temperature.
Mr Smith spent 11 weeks in intensive care and was discharged, but weeks later returned to hospital as he had not made a full recovery.
He died from sepsis on November 1.
Following his death the trust carried out a root cause analysis, which revealed a string of failures relating to Mr Smith's treatment.
The inquest continues.