More than 100 people have been struck by the illness in recent weeks.
Mr Campbell said the latest evidence showed an "almost negligible" level of cryptosporidium in the public drinking water.
Speaking on Friday, he said: "There is some concern within the general public over the whole cryptosporidium issue, particularly when up to a year ago there was really very little evidence of it.
"But the facts, as the public health offiicials tell me, is that there is a background level of cryptosporidium in the water on a continual basis."
'Impossible to eliminate'
It is the second time in 12 months that an outbreak of the bug has been traced to the water supplied to south and west Belfast.
Mr Campbell said cryptosporidium could not be eliminated no matter what measures were used to tackle it.
He said there were other factors outside of the public water supply which were sources for cryptosporidium.
The minister said it was essential to find adequate resources to implement "barrier treatment".
The Northern Ireland Eastern Health Board confirmed on Thursday that 106 people had now become ill.
On Wednesday the Northern Ireland Water Service said it had identified the source of infection of the cryptosporidium bug.
Incubation period
The team investigating the outbreak believes it has traced its origins to the Dunore Point Water Treatment Plant on the eastern shore of Lough Neagh.
It is understood the contamination was caused by a blocked drain which allowed untreated water into the filtration system.
The illness has an incubation period of a week to 10 days, so public health doctors are expecting further cases.
The cryptosporidium parasite can cause vomiting and chronic diarrhoea, and is particularly debilitating for the elderly, young children and the sick.
It can also prove fatal.
Health experts say cryptosporidiosis in immuno-compromised people often results in a chronic life threatening gastro-enteritis with a high mortality rate.
Special team
However, Dr Brian Morgan, the Eastern Board's consultant in communicable disease control, said he was satisfied that there was no further risk from drinking tap water.
He said: "I think this must be described as a very unusual set of circumstances, which in fact resulted in a combination of events - of themselves each unusual - which combined to cause a contamination which is extremely unusual.
"I am absolutely convinced that the water supplied to the Belfast population now is absolutely safe.''
The discovery follows an increase in the number of cases of the stomach bug in south and west Belfast.
Eighty-nine of the 106 cases have emerged since the end of February.
A special team has been set up at the Water Service's Communicable Disease Surveillance Centre to investigate the new outbreak.