The Government has ramped up pressure on teachers threatening industrial action to reconsider their position.
As disputes over pay intensify with secondary school teachers refusing to work outside normal hours, Tanaiste Eamon Gilmore warned there will be no renegotiations.
He also urged the Association of Secondary Teachers of Ireland (ASTI), which confirmed it will not meet parents before or after school after its members rejected the Haddington Road agreement, to think about their pupils.
"The students who are attending secondary schools are entitled to their education," Mr Gilmore said.
Mr Noonan said there was "no scope" to change the agreement, while Mr Howlin insisted the adjustments made through the pay deal were essential in the framing of the forthcoming budget.
"The agreement is there. Obviously it has been implemented from July 1," Mr Howlin said.
"We need the savings. It's part of the budgetary arithmetic. I would ask people to reflect upon it.
"None of this is easy. None of the work we are doing is easy. But it's not changeable."
The public expenditure minister added it was "remarkable" that only one union remains "outside the loop" on the pay arrangement.
Other teaching unions, including the INTO and the Teachers' Union of Ireland, have supported the Haddington Road agreement which will change pay and working regimes across the public service.
The ASTI announced yesterday that teachers will refuse to hold planning and policy development meetings and in-service training unless it is during the school day.
The 17,000 members of the union plan to begin the industrial action on October 2.
The decision was announced after leaders of the ASTI met to discuss enforcing a ballot of teachers in favour of the action, up to and including a strike.
The union said while teachers are anxious not to disrupt their students' education, the vote had been two to one in support of the action.
The ASTI said its members are being directed not to undertake any duties arising from vacant middle management posts unless they receive pensionable pay for the work.
The Tanaiste added: "The Haddington Road agreement was negotiated with all the trade unions.
"It is in place now. The ASTI have chosen not to accept it and the Government has to accept that."