Nicky O'Leary, a Dublin psychologist, said that teachers did not know how to deal with highly able children.
"Some teachers get an hour on highly able children during their initial training, many get no training at all," she said.
"Our Irish solution to this problem, therefore, is that these children do not exist."
Dr O'Leary said that gifted pupils often preferred not to have their exceptional abilities recognised.
"They love being gifted but they don't tell people about it," she said.
"They zip it because they don't want to be teased."
When she asked one boy why he did not put his hand up in class, he replied:
"I know the answer, the teacher knows I know the answer but, sure, the teacher has to teach the other 26 kids."
Some of the 43 exceptional pupils that Dr O'Leary interviewed were less sanguine about the "problem" of being the brightest in the class.
They sometimes became frustrated or badly behaved and caused problems for their parents. They all had IQs of at least 145, but none of them enjoyed school.
One primary-age boy said he had asked his teacher for extra work but she had not obliged. "I'm counting. I've asked seven times," he said.
Dr O'Leary said teachers should be trained to work with parents and other professionals to help highly able pupils.
She said: "I also think our gifted children need to be a little more unreasonable. As George Bernard Shaw said, 'The reasonable man adapts himself to the world around him. The unreasonable man expects the world to adapt itself to him. Therefore all progress is made by unreasonable men.'"
Her co-presenter, Margaret Sutherland of Glasgow university, said that highly able Scottish children had also had too little help and attention.
"In Scotland, if you are 13 and you can't read then people, including teachers, don't want to know.
"If you are three and can read, it's the same - nobody wants to know."
But she said the code of practice that accompanied last year's Additional Support for Learning (Scotland) Act had provided grounds for optimism.
It had acknowledged that more able young people need "more challenging provision".
"For the first time, the legislative context in Scotland would seem to offer a framework in which the needs of high-ability students can and should be met within mainstream education," she said.