William Booth said there were "deficiencies" in the care Sean Turner received during March 2012.
Sean suffered a brain haemorrhage and cardiac arrest six weeks after he had undergone corrective heart surgery.
"I can accept there were deficiencies in care and that the [staffing] ratios could have been better," Mr Booth said.
The hospital's matron and lead nurse for paediatric critical care services, added the facility would not endanger children by moving them.
"We would never move a child from intensive care to a ward if we thought it was unsafe for them to be there."
Mr Booth told the court changes had been made on Ward 32, a specialist paediatric cardiac ward, where Sean was taken after intensive care, but insisted they were not as a result of his death.
"The changes have not been made as a direct result of Sean Turner but, of course, there are lessons learnt and we have addressed those in relation to how Ward 32 operates," Mr Booth said.
The inquest has heard that following Sean's death, and that of seven-year-old heart patient Luke Jenkins, from Cardiff, who died nearly a month later, their parents complained to the independent healthcare watchdog, the Care Quality Commission (CQC).
The CQC performed an unannounced inspection and issued a formal warning to the hospital about standards on Ward 32.
Adam Korn, representing Mr and Mrs Turner, suggested there was a direct correlation between the deaths of the two boys, the CQC report and recommendations and the changes made on the ward.
Mr Booth said he did not accept this and added: "The trust had already undertaken a risk assessment and identified there were issues with high dependency and staff levels, which is why the trust commissioned the independent review.
"I would not agree it was as a result of these deaths," he added.
Steve and Yolanda Turner, from Warminster, Wiltshire have accused doctors of transferring their son to Ward 32 from intensive care too soon and said they missed the signs of his worsening condition.
Up to 10 families are believed to be taking legal action against the University Hospitals Bristol NHS Foundation Trust over treatment on Ward 32.
The inquest at Avon Coroners's Court at Flax Bourton, near Bristol, continues.
A four-year-old boy who died after heart surgery at Bristol Children's Hospital received a poor level of care, a senior nurse told an inquest.