The Catholic Archbishop of Dublin, Dr Diarmuid Martin, has expressed concern that the religious presence in privately-run secondary schools could become predominantly associated with educating an elite.
The archbishop also said it was regrettable that the Catholic ethos of schools was often "portrayed as a kind of ideology, set within an ideological battle".
Education, he said, "should never be seen merely as a form of economic investment".
Speaking in the Church of the Sacred Heart in the west Dublin suburb of Huntstown during the annual schools' Mass, he said accountability in education was "not necessarily a bad thing".
But real difficulties arose when it came to determining "what constitutes the 'best education' and how schools are ranked".
"How are we to value the achievements of schools and teachers who work with students who, because of disadvantage or inequality of opportunity, could not easily aspire to the highest Leaving Certificate grades?"
He added: "We must be attentive as a society that we do not allow a system of evaluation to emerge that would, perhaps inadvertently, privilege a utilitarian understanding of education. Education cannot be judged exclusively in terms of quantifiable economic or technical outcomes."
Catholic schools may be in need of their own instruments of evaluation, he said.
"I would personally be concerned, for example, if the religious presence in voluntary education were to become predominantly associated with the education of the elite."