The Roslea surgery closed last week, leaving the village without a doctor for the first time in 100 years.
Several hundred people who attended the meeting were told that no doctors applied to take over the contract.
Patients will now have to travel to the health centre in Lisnaskea.
"It will have a very, very serious impact on me because we have a member of the family who isn't in very good health," said Rosemary Mulligan.
"I have to go to the doctor a lot about this person and then have to go on a round trip of over 30 miles for any medication or anything I need."
She added: "We had a lovely doctors and everything was going well and they were coming from Lisnaskea and we were happy enough and now its gone. We're angry and we're sad."
Jimmy Flynn had a hip replacement in November said it was "a terrible mistake that we haven't got a surgery".
"I'm 87 years of age and it's not a good idea for me to have to drive down to Lisnaskea.
"We're hoping that this meeting will maybe entice somebody to come back here to Roslea."
Ann Began said it will lead to increased waiting times for appointments.
"You could be waiting three weeks if you want to see a particular doctor," she said.
"I think it's terrible because the area goes right out to the border and old people are going to have to travel and they mightn't have transport.
"Not everybody can drive. I just think it's awful."
Representatives from the Health and Social Care Board said they had found it increasingly difficult to replace retiring GPs in rural practices, as doctors no longer want to work on their own.
They said this contrasted to the situation 20 years ago when there were about 40 applicants for a GP post in the nearby village of Newtownbutler.
Maple Health Care has taken over the patients of three single-handed practices in Roslea, Newtownbutler and Lisnaskea.
Dr Sloan Harper, director of integrated care at the Health and Social Care Board, said the temporary model of a GP from Lisnaskea providing services in Roslea for part of the week was not sustainable in the long term.
"It will mean some inconvenience, unfortunately, for a small number of patients living in the Roslea area and the board is disappointed that we haven't been able to continue that service," said Dr Harper.
"The doctors working here are taking on a major change process, going from a practice of 8,500 to 14,500 patients, taking over three practices.
"So it felt safer and more sustainable for them to work out of two sites, and so Newtownbutler - being the larger premises and having better car park arrangement - was felt to be doable.
"To spread their medical and nursing workforce, its not just about a doctor going down there... it was felt that was too big a stretch and so we feel the current arrangement is the best option available."
Dr John Porteous from Maple Health Care in Lisnaskea, who has been a GP in Fermanagh for 29 years ,said there were so many GP vacancies that "the least attractive practices just have no hope whatsoever".
He added that for newly-qualified doctors, working alone in a small surgery in an isolated community would not be viewed as a "comfortable experience".
They would prefer to work somewhere "where they can share the responsibility, where there would be safety if something were to go wrong", he added.
"They've come through training practices where there would be quite a number of doctor and nurse colleagues, there would be lots of extra help on site.
"I'm a Fermanagh man all my life and my own dad was a single-handed GP for many years and, of its time, it was a good model but practice has become so complicated and the pressures are so high that I think you're going to find increasingly doctors are going to come together and form larger groups.
"Almost inevitably that will mean small villages will no longer have the local surgery and you will have fewer, larger health centre hubs."
The long-term future of single-handed rural practices is "unsustainable", a public meeting to protest against the closure of a County Fermanagh GP surgery has been told.