Mr Heaton-Harris made a budget statement on Thursday within the absence of a Stormont Executive.
The government has not been reformed because the last Assembly election in May due to DUP protest motion against the Northern Ireland Protocol.
Ministers with restricted powers remained in post till the top of October, when the deadline to kind a brand new government passed.
Sinn Fein MLA Conor Murphy said the collapse of Stormont had left departments struggling to management spending and a one-year budget set in direction of the top of the monetary year.
“This is hugely damaging for public services, particularly the health service which desperately needs financial certainty,” he said.
Mr Murphy additionally criticised a scarcity of further charges reduction for companies and queried whether or not sufficient had been allotted to permit pay rises for public sector staff.
“It is not clear from the British Secretary of State’s announcement what is happening with public sector pay. I will urgently be seeking clarity on this matter,” he said
Alliance Party deputy leader Stephen Farry reacted to the statement by warning there have been troublesome instances forward by way of public spending in Northern Ireland.
Mr Farry described as “regrettable but inevitable” that it fell to the Secretary of State to set the budget.
He said Mr Heaton-Harris’s statement offered a “basis for the continuity of public services”, however with Stormont collapsed, there was “little scope for strategic decisions to be taken to reform public services to make them more sustainable”.
“The future of resources for the Block Grant in the years ahead, as outlined in last week’s autumn statement, is to flatline,” he said.
“Some very difficult times are ahead in terms of public spending here.
“Regrettably, the opportunity to fix the roof when the sun was shining hasn’t been taken in recent years.
“We should be much further on in reforming public services and tackling the costs of a divided society to free up resources for reinvestment. Options on revenue-raising also need to be considered.
“Those considerations are now going to have to be accelerated in a much more difficult governance and financial context.”
UUP finance spokesperson Steve Aiken said Northern Ireland was “facing a deeply challenging period financially”.
“The statement from the Secretary of State reflects that. We will take our time to analyse the detail and implications of the statement, but it is a clear example of why we need to see the executive back up and running,” he said.
“The challenges caused by soaring energy costs and inflation are affecting every home in Northern Ireland.
“Local ministers being able to provide a multi-year budget will be vital in producing solutions that work for people in Northern Ireland.”
SDLP leader Colum Eastwood blasted a “Tory budget that will lead to stark cuts to education and other areas of public spending”.
“The DUP has handed Chris Heaton-Harris the power to make these decisions. And the spending decisions of other ministers have given him the cover to make cuts to critical areas of public spending,” he said.
“The transparent threat to introduce new revenue-raising measures in the absence of agreement to form an executive will lead to further hardship for ordinary people who are already being hit again and again with food, fuel and energy bills that are smothering family finances.
“Further pain is not inevitable, power that should never have been given to him can be removed from the Secretary of State.
“But it requires the DUP to acknowledge that the consequences of their protest are now inflicting unsustainable pressure on ordinary people, and on the education of our children.
“People across Northern Ireland can no longer afford to pay the price for this political selfishness.”