Saleem Haj-Yahi, a heart-transplant surgeon with the National Advanced Heart Failure Service, said he and his consultant colleagues believe patients are missing out on treatment which could transform their lives.
A special strategy to promote the service was launched last year after concerns that the low number of heart transplants performed in Scotland was not a true reflection of the numbers who need the operation.
Since then, Mr Haj-Yahi said, referrals to the centre at the Golden Jubilee National Hospital in Clydebank had increased.
However, he and his colleagues still fear they are not seeing all the patients who could benefit from either a transplant or implantation of a Ventricular Assist Device (VAD) – known as an artificial heart – which can help the struggling organ.
He also says some patients are referred when they are already too ill to cope with transplant treatment.
He spoke out ahead of a special event at the Golden Jubilee today to mark 20 years of heart transplants in Scotland.
In heart failure the organ cannot pump blood around the body properly. Those with advanced heart failure die without treatment.
From 1986 to 2003, 3000 patients under 65 were hospitalised with heart failure for the first time each year in Scotland. A thousand of them died within a year.
In 2011-12, after the launch of the strategy, nine heart transplants were performed. So far in the current financial year, there have been three.
Mr Haj-Yahi said: "We do not have a problem with our capacity. We are very happy to accommodate increasing number of referrals and transplants. We have a target to do more heart transplants because we are certain the figures have told us there are many more patients who need heart transplants and they are not being referred – and they are not being referred in time."
He said the problem was in making clinicians in other Scottish hospitals aware what the National Advanced Heart Failure Service could do for very sick patients.
Just two or three years ago when VADs were not readily available, he said, clinicians "gave up" on these people.
He said once referring cardiologists saw a dying patient recovering well with a transplant or VAD, they would refer more. He added that the service was also happy to accept referrals from nurses and junior clinicians and had in one or two cases dealt with patients who had arranged their own referral.
He said: "The most important message is not to hesitate to refer patients an early stage for consultation.
"It does not make them or the patient commit themselves for anything. At least a second expert view will always be helpful. That is true in every aspect of medicine.
"It is quite important that physicians and cardiologists have very low thresholds to send these patients and do not wait until the patients are too sick."
More than 160 patients and staff are attending the anniversary celebrations at the Golden Jubilee today.
A Scottish Government spokesman said: "The Golden Jubilee is working hard to increase the number of referrals to their transplant service by raising awareness and ensuring clear guidelines for these therapies are available across Scotland."
lScores of transplants are stopped each year when families override patients' wishes to donate organs, a survey has found. Four out of 10 potential organ donors, including many on the organ-donors register, cannot save lives when they die due to objections from relatives.