An 11-month-old girl was the second patient to die from an overdose of the same drug at a Surrey hospital within six months, an inquest heard.
Sophie Burgess died after being given the anti-seizure drug phenytoin at St Peter's Hospital in Chertsey in June 2016.
Another patient died after receiving a "significant" overdose of the same drug in January, an inquest in Woking heard.
The hospital's head of patient safety said the drug was "very complicated".
Dr Paul Murray told Surrey Coroner's Court the death in January 2016 was investigated as a "prescribing error".
Asked if staff should have been told to be cautious when using the drug following the January incident, he said: "I wish we had done."
He said "major work" had been undertaken at the hospital to improve the safe use of the drug.
The court earlier heard it had been decided Dr Lojein Hatahet would administer the drug to baby Sophie from a handheld syringe after an automated syringe-drive failed, despite the objections of a nurse.
Paediatric consultant Dr Mohammed Rahman, giving evidence as an expert witness, said the drug should be administered at 1 milligram per kilogram per minute, but added that it would be "difficult" to follow those guidelines when injecting it manually.
He would expect any paediatrician to know that the risk of "cardiovascular collapse" was "very real" if the drug was given too quickly, he told the court.
Fiona MacCarthy, the paediatric consultant who prescribed the drug for Sophie, had amended her records to show the drug was administered for an extra 10 minutes than was previously recorded, the court heard.
"Were you trying to cover your tracks because you knew you had given phenytoin too quickly, asked Clodagh Bradley QC, representing Sophie's parents.
"That is incorrect," Dr MacCarthy replied, adding that the initial entry was an estimated time which she later amended after speaking with Dr Hatahet.
The inquest was suspended in 2017 while Surrey Police officers re-examined their investigation after fresh expert evidence emerged.
The force decided not to proceed with criminal investigations and the inquest recommenced on Thursday.
Dr MacCarthy was not part of Surrey Police's investigation, her legal representative Andrew Hockton said.
The inquest continues.