The confusion centred around the term braindead, Mr Keep said, and the fact that organs such as the lungs, liver and heart cannot be removed if a patient's heart has stopped.
The call was made in an editorial in the Royal College of Anaesthetists' journal, Anaesthesia.
But the founder of the British Organ Donor Society said such comments could be "very unsettling" for bereaved relatives.
"The sooner we scotch the thought of pain and the person being alive in any sense of the word then the better," said John Evans.
Mr Evans said it was his understanding that brain-stem dead patients were often already anaesthetised prior to surgery to prevent "involuntary reaction".
"It has been the practice for anaesthetists to anaesthetise the donor patient - not as much as the living patient because the issue of pain doesn't arise - but sufficiently to avoid there being an involuntary reaction."
There are differing schools of thought as to whether a patient, certified brainstem dead but whose heart is still beating, can feel pain.
Philip Keep, a consultant anaesthetist at the Norfolk and Norwich Hospital, said earlier: "Almost everyone will say they have felt uneasy about it.
"Nurses get really, really upset. You stick the knife in and the pulse and blood pressure shoot up.
'Wriggling'
"If you don't give anything at all, the patient will start moving and wriggling around and it's impossible to do the operation."
Speaking on BBC Radio 5 Live, Mr Keep said he was in favour of transplantation but would not carry a donor card because of his concerns about the way in which organs were obtained.
"If I knew that somebody was going to give me an anaesthetic, before my donor organs were removed, I would carry a donor card and I think a lot of other people who have got these doubts would carry a donor card as well."
The confusion centred around the term braindead, Mr Keep said, and the fact that organs such as the lungs, liver and heart cannot be removed if a patient's heart has stopped.
"You have to keep the patient's heart beating all the way through the operation until the organs have been removed," he said.
Last year guidance from the Intensive Care Society said the administration of an anaesthetic on organ donors was unnecessary.
But Basil Matta, of the critical care unit at Addenbrookes Hospital in Cambridge, said: "Death is not an event but a process and our limited understanding of the process should demand caution before assuming that anaesthesia is not required."
Rules on what constitutes brain death were formed by the royal medical colleges in 1976 and 1979.