Dr Christiaan Slabbert told police his failure to "retain the decimal point" more than 14 hours into a 24-hour shift led to Benjamin Adams receiving a massive overdose of the cardiac drug Digoxin.
The South African doctor told the baby's parents, Carl and Tina Adams, he was "sorry" when he appeared at the inquest in Kidderminster, Worcestershire.
Dr Slabbert, who now works in Arkansas, in the United States, refused to answer questions on the advice of his barrister, but when asked by the Adams' family solicitor, Paul Balen, if he wished to say anything to the parents, he replied simply: "I'm sorry".
Tina Adams, 25, who now has a nine-month-old son, broke down as the doctor left the witness box.
Benjamin was just a few hours old when he was given 10 times the recommended dose of Digoxin at Alexandra hospital, Redditch, in April 1997. The blunder happened after the baby developed respiratory problems and a fast heart beat shortly. He had been born by Caeserean section on 25 April.
Doctors at the hospital's paediatric department sought advice from cardiologists at Birmingham Children's Hospital, who recommended thedrugs adenosine and Digoxin.
Adenosine was to be prescribed at a rate of 100 mcg per kilogram of the baby's weight and Digoxin at 10 mcg per kilogram, the inquest heard.
The dosage was written on the patient notes by the senior physician, Dr Neel Kamal. Dr Bridget Wilson and Dr Slabbert were left to write up the prescription, the hearing was told.
The adenosine was administered by Dr Wilson and began to improve the baby's condition.
The Digoxin was then administered by nursing staff working from the prescription written by Dr Slabbert. In a statement to police at the time of the incident, Dr Slabbert, 38, said he had been tired when he made the mistake, and was on his second 24-hour shift during the week of the death.
The statement read: "I had had a demanding day. I was on duty for a 24-hour period. There was a degree of tension due to the bed and staff shortage."
The doctor, who told police he had "no real experience" of prescribing intravenous cardiac drugs, was called to several births, received referrals from GPs and attended to patients in casualty during his shift, before being required to write the prescription.
He told police: "I then made the calculation but inadvertantly failed to retain the decimal point.
"I was quite tired, having been on duty since 9am the previous morning and working continually without much of a break, I had not even been able to have an evening meal."
The Alexandra Healthcare Trust has admitted liability and the family, of Fir Trees Close, Batchley, Redditch, have received pounds 7,500 compensation, the maximum payout for the death of a child.