Sally Johnson, director of organ donation and transplantation at NHS Blood and Transplant, said: "We would like to send our sincere condolences to Tiarna's family at this very difficult time following the loss of their daughter.
"It's so sad to hear that she didn't receive the vital organ she needed to give her a chance of life.
"It is always tragic when when anyone doesn't get the organ they need but, the sad reality is that until we are all prepared to agree to donate our organs of those of our children after death, people will sadly die waiting for a transplant.
"Current national guidelines for the diagnosis of brain death do not support donation from brain dead infants under the age of two months, so we would support the review of the current guidance in the light of medical advances and increased knowledge."
A baby has become the youngest in the world to be supported by a Berlin Heart device.
Tiarna Middleton, 14 days old, from Rowlands Gill in Gateshead was born on May 22 with an extremely rare heart condition.
It was decided she would not survive and doctors at the Freeman Hospital decided to use a new small Berlin Heart Ventricular Assist Device - which was delivered from The Berlin Heart Company in Germany where it is made.
On Tuesday, surgeon Massimo Griselli fitted Tiarna with this device which doctors hope can keep her alive until a donor heart is found.