The Tánaiste says he does not accept that children who go to private fee-paying schools have a better chance of getting a job.
It comes after school 'league tables' highlighted the best schools for feeding to universities based on Leaving Certificate results.
They show students from fee-paying schools and gaeilscoileanna claimed the highest number of places in courses with the highest points.
The Irish Times Feeder Schools list says there is little difference between the performance of fee-paying and State schools in the overall list.
But it says that the list of schools which send students to high-points courses in universities and other colleges is almost entirely dominated by fee-paying schools.
In the list the top nine schools are all fee-paying, while seven of the remaining top 20 schools are also fee-paying.
The Irish Times says that there is a consistent annual pattern in the lists and suggests the highest-earning professions have a higher proportion of people who went to private schools.
But Eamon Gilmore says there is nothing wrong with the free education system.