He also said he feared the numbers could have been underestimated.
In an interview on RTÉ radio’s Today with Claire Byrne show, Dr Martin said that when he was Archbishop he “simply had to throw the files on the ground” when he read upsetting reports.
“I'm extraordinarily struck by the numbers in the special schools. I think that sexual abuse of particularly vulnerable children is very shocking and that the second thing is that the numbers are very high.
"For example, if you look at the three paying schools, one of the reasons for this is that I think most people may have thought this scoping inquiry was primarily about those schools. And this would mean, I think, that the numbers regarding other schools is probably under underestimated and probably higher.”
Dr Martin added that he had been pleased to see a garda statement asking people to come forward. “I think if people realised they would have a safe and friendly reception, they would come forward. And the more we learn about this, I think in the long term it's better.”
One of the most important aspects of any inquiry was to examine the area of safeguarding, he said.
“Sexual abusers don't abuse small children because they're sexually starved. They're only interested in abusing small children.”
The moving of known abusers was something that he found “very hard to stomach.”
While he dealt with many “fires” over the years, the people for whom he had the highest regard were “poor, ordinary working-class women who came to my predecessors and said to them, I would not like any other child to have to go through what my child did, and they were not listened to.
“They were never going to send their children to fee-paying schools, but they knew what it meant to abuse a child.”
The damage from abuse was more than the actual physical or sexual abuse, he said.
“It takes away the entire self-esteem of a child. The abuser is actually saying to a child, ‘I could do anything I like with you, you are worthless’. And that's the thing that drags right throughout their life.
"And then the sexual abuse of a child isn't, doesn't just damage the child, it damages parents, spouses, generations, children. It's an extraordinary thing. The numbers and the incidences are frightening. But the reality is much greater, that’s the sad thing.”
Great damage had been caused by some orders who took decisions to safeguard their own institution, he said.
“Not only did they do immense damage to children, they also damaged the good name of the backbone of their own institutions, which are their own brothers, sisters who do good work and were blameless in the law.”
Dr Martin said he believed one way forward was for the government to establish a lead public government figure to take charge of the issue.
“The Irish government is not too good at joined up thinking, and we should have some person, some senior person in government who says ‘I will stand up, carry the flag and take responsibility to explain where we are, where progress is being made, where the obstacles are’, that people can turn to them.”
This was not to absolve religious orders of responsibility, but the lead had to come from the state, who could ensure that the orders carry out their responsibilities.