NASUWT NI president Susan Parlour made the comments during a speech to members at the union's annual conference.
She also said the Education and Training Inspectorate, which carries out school inspections, was "not fit for purpose".
The NASUWT is one of the largest teaching unions in Northern Ireland.
Its members are currently engaged in rolling strike action over pay and workload, along with members of the INTO union.
National officer Justin McCamphill also spoke at the union's annual conference in Belfast, warning of further strike action if devolution was not restored.
Teachers were prepared to fight for adequate budgets for schools and against the erosion of teachers pay, he said.
In October 2016, all teaching unions in Northern Ireland rejected an offer that saw pay frozen in 2015-16 and a rise of 1% for 2016-17.
Ms Parlour was heavily critical of what she called "political myopia and a penny-pinching approach to education".
"The so-called fresh start agreement, rather than living up to the positive promise of its name, has brought stagnation and rot to classrooms," she said.
She also claimed that front-line services, including those for children with special educational needs, had suffered due to budget reductions.
"This clearly suggests that we have politicians here in NI who know the cost of everything and the value of nothing," she said.
"While these cuts were being imposed mercilessly on our schools, let's not forget that our government saw fit to send millions of pounds up in smoke in the flawed RHI scheme."
In January, former Education Minister Peter Weir said that schools needed an extra Â£240m over the next three years just to maintain current spending levels.
He also warned that schools faced making "redundancies and savings".
"Efficiencies in and of themselves will not be enough to avoid the sort of pain that will be there if there is no new money at all," he warned.
Subsequently, 15 primary school principals from County Down wrote a joint letter to parents warning their schools were facing "financial disaster".
Further cuts to the education budget will make Northern Ireland's education system "unsustainable," a teachers' union leader has said.