Ian Hutchinson had been been left looking after seven-week-old Kieron after his wife went shopping. The little boy had been declared fit and healthy after undergoing his six-week check-up just hours before, but went on to suffer a traumatic brain injury whilst in his father's care, and died four days later in hospital.
Hutchinson said he had tried to change Kieron's nappy after his wife Rebecca, 21, had left, but could not find any baby wipes. He told doctors and police that his son had became upset, then coughed, went quiet and stopped breathing.
Bryan Cox QC for prosecution told Sheffield Crown Court that experts said Kieron's injuries could only have been the result of non-accidental trauma.
Mr Cox said: "What caused the defendant to inflict such serious injury to Kieron is not clear. It may have been as trivial as a sense of frustration that he'd been alone with Kieron without the wherewithal to change his nappy."
An ambulance attended Hutchinson's mother's house in Sheffield on September 3 last year after a neighbour heard Hutchinson's yelling for help. The prosecution said a nurse later heard the defendant tell his wife: "I'm sorry. I'm really sorry."
Hutchinson denies murder. The trial continues.
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