The group was found when a Stena Line ferry from Cherbourg arrived at the port on Thursday, and all of them are safe and well.
“Thank God there were no fatalities because it was an extremely lengthy journey,” said IRHA president Verona Murphy.
“To be confined in a small, mostly immobile space where there is very little air is something that could have ended in tragedy.
“Our biggest concern is that it is a humanitarian disaster and very little is being done about it.”
Members of the group were medically assessed soon after they were found on Thursday and all were declared reasonably fit and well.
They were brought to Dublin, where their claim for asylum will be processed.
Ms Murphy said it was unusual to discover such a large group of people who made the 17-hour sea journey to Ireland.
“Yes I am afraid that there are people who come in undetected, but not necessarily in these numbers,” she said.
Earlier this year, authorities at Rosslare discovered 14 people, including one juvenile, inside a refrigerated unit but they were unharmed.
Ms Murphy said haulage operators were suffering financially because the refugee situation was driving up the cost of insurance.
“We are suffering,” she said. “We are working at the moment off very low-profit margins and each time an incident occurs there is an excess that has to be paid on the insurance.”
Hauliers in Britain have to pay on-the-spot fines of £2,000 for each migrant found on board their vehicle, but such penalties are not applied in Ireland.
“The container in which the group was found was dropped in the yard at Cherbourg. It was then put onto the ship,” said Ms Murphy.
“We don’t know where or how the migrants got into the container; it could have happened when it was on the ship or if someone else put them in the trailer.”
Immigrant Council of Ireland CEO Brian Killoran said other migrants may have managed to get into Ireland undetected.
While such incidents were “quite sporadic” it showed that people were desperately trying to look for a way into another country so they could feel safe.
Mr Killoran, who was speaking on RTÉ Radio, said the group were in a curtain trailer. Had it been a refrigerated unit they might not have survived.
He said the group should be allowed to stay in Ireland because sending them back to where they had come from was not an option.
The International Organisation for Migration showed 111,000 crossed the Mediterranean this year and 2,500 lost their lives.
“That is the equivalent of about six 747s plunging into the Mediterranean so far this year. It is a massive loss of life,” said Mr Killoran.
He noted Ireland had only taken about 30% of the 4,000 refuges that Ireland pledged to take in by September.