Director of the Catholic Education Service Paul Barber was speaking after new research showed that children from poor families are missing out on places at the best primary schools.
He told Premier's News Hour the schools have some responsibility towards changing this.
He said: "Making sure that the admission policies are as fair and inclusive as possible so that we make sure that the schools serve all of the community, including those in the most deprived areas."
Families on low incomes were four times more likely to send their children to a primary school that the regulator judged as needing improvement than the wealthiest families, the study revealed.
It also found that poor families were found to have less than half the opportunity to send their children to a school rated as outstanding by Ofsted.
Areas with the highest proportion of outstanding schools also had average rents double that of those with the lowest share, researchers said.
The analysis was carried out by Teach First, a charity that supplies highly-trained teachers to struggling schools in deprived areas.
Paul Barber said accusations the complex applications process for faith schools are partly to blame are untrue.
"That's often said, but it conflicts completely with the evidence," he said. "The evidence says that's entirely untrue - so for instance, our secondary schools, there are 47% more children from the poorest 10% areas than there are across schools nationally."
Tim Crow was a head teacher at the River School a Christian independent school and is now on the board of governors. He told Premier richer parents are forcing poorer people out of some catchment areas.
He said: "Parents want the best for their children, so if the reputation and the records seem to suggest that 'school x' is excellent, they will of course want to get their children into that school.
"Some will take any necessary steps to ensure they gain access."
Teach First said there were signs of progress, notably in Manchester, Middlesbrough and London.
The Department for Education added that there was now a record number of children in good or outstanding schools, up 1.4 million from 2010.
It said it plans to improve standards across the board by increasing the control teachers and school leaders have, alongside other measures to tackle failing and "coasting" schools.
A spokesperson added: "We are backing schemes like Teach First and the National Teaching Service to get great teachers where they are most needed."
Listen to Premier's Aaron James speak to Paul Barber here: