梅先生告訴代表們，雖然可以採取 "許多行動 "來 "使衛生和社會保健更加高效和有效....，但我們決不能假裝僅靠效率就能縮小需求和供應之間不斷擴大的差距。"
On Friday, the trade union said its members in Northern Ireland, England and Wales would walk out on 15 and 20 December in a dispute about pay and staffing levels.
Mr May told the annual conference of the Northern Ireland Branch of the Healthcare Financial Management Association in Belfast it was getting harder to deliver what people needed.
"With the resources available to us, we are finding it increasingly difficult to deliver the health and social care system needed to meet all the demands of the population," he said.
"We all want to get back to a health service that provides timely care to everyone who needs it when they need it.
Mr May told delegates that while "many actions" could be taken to "make health and social care more efficient and effective….we must not pretend that efficiencies alone will close the widening gap between demand and supply."
Mr May added: "The reality is also that our ageing population and advances in medical science mean the gap between demand and capacity is growing year-on-year, winter-on-winter."
"At the same time, many people requiring less time-critical care are having to wait much longer - often in pain and discomfort. This is not the level of care that the public expects or that any of us wants to provide."
Revealing details about its strike action, Pat Cullen, the general secretary of the Royal College of Nursing, said nursing staff "had enough of being taken for granted, enough of low pay and unsafe staffing levels, enough of not being able to give our patients the care they deserve".