The New Cross Hospital in Wolverhampton has also decided to keep all children under two in the observation unit overnight unless parents explicitly request otherwise.
Chelsea Greet became the fifth child victim of a form of the disease in the past two months when she died in the early hours of Monday.
Her parents Paula Duffy and Wayne Greet of Woodcross Lane, Woodcross, Wolverhampton, issued a joint statement tonight with Dr Simon Walford, medical director of the Royal Wolverhampton Hospitals NHS Trust.
It said Chelsea was admitted to hospital about two weeks before her death and was seen by at least three specialists. She had blood poisoning and was also thought to have meningitis.
She was treated, apparently made a good recovery, and was allowed home from hospital last Thursday.
The antibiotic course continued but her condition deteriorated and her parents took her back to hospital on Sunday afternoon.
She was admitted to the children's unit observation ward for about five hours but two doctors decided there were no signs of serious illness and recommended to the parents that they take her home.
"The hospital regrets the decision to send Chelsea home. To avoid a similar circumstance arising again, the policy in the observation unit has been changed to prevent the discharge of babies below the age of two in the evening unless at the explicit request of the parents," Dr Walford said "It was a terrible tragedy. The difficulty is to try never to get it wrong but that is what happened in this case.
"It was a well-intentioned decision that was a mistake. We acknowledge that, and I think the family has, too."
A spokesman for Wolverhampton coroner's office said a post mortem examination was conducted on Thursday but the full result would not be known for about three weeks.
Other children to have have died recently from meningitis are Ryan Blow, 19 months; Adam Lucas, 20 months; Emma Harris, 5, and Alexandra Yates, also 5,both from Sussex.Reuse content