The vast bulk of teachers believe the ban on recruitment has impacted on schools' ability to deal with disruptive students.
The Teachers Union of Ireland (TUI) called for the staffing freeze to be reversed amid claims the devastating impact of cuts is having the biggest effect on the most vulnerable students.
But Education Minister Ruairi Quinn has warned that the Government cannot go back on the ban on filling promotional posts.
"It's an understandable request, but the provisions that were communicated to the schools, including the decision on the moratorium, will not be changing," he said.
Although a lifting of the moratorium is off the table, TUI president Bernie Ruane said the block on filling senior posts leaves schools unable to meet many of the health and safety requirements.
"For many students, the classroom is the only safe place they know and they are now being denied the critical pastoral services of positions such as year head," Ms Ruane said. "This block on filling of positions is having a particularly bad effect on the most vulnerable students in the education system."
The TUI, which is holding its annual conference in Tralee, Co Kerry, estimates that on average more than two assistant principals have been lost from schools over the last two years.
A study by the union during March found that 79% of principals believed the non-filling of positions had a high to medium impact on the ability of the school to address discipline and behavioural issues, with 46% saying it had a high impact; 72% stated that the loss of promotional posts had a high to medium impact on the provision of pastoral care and tutorial support.
Mr Quinn said the challenge on a tight budget would be to redeploy teachers to where they are needed while making savings.