An energy price cap has been announced for homes in Northern Ireland from November, while home heating oil customers are to get a one-off payment of £100.
The Government has also said Northern Ireland businesses will benefit from an energy cap on an equivalent basis to a scheme announced for the rest of the UK.
Sinn Fein minister Mr Murphy said no clarity had been provided to businesses about when they would receive assistance with bills.
Mr Murphy said: “This doesn’t go far enough given the huge increase in energy costs in the last year.
“Seventy per cent of households who use home heating oil will find the news that they will get a mere £100 of support for their fuel bills this winter insufficient.
“It is disappointing there has been no update on when households here can expect to receive their £400 Energy Bill Support Scheme payment.
“The promise of equivalent support without the underpinning detail does nothing to reassure businesses.
“Most businesses are anxious about how they will make it through the winter.”
Mr Murphy said the absence of an executive at Stormont is negatively impacting people and businesses in Northern Ireland.
The Stormont powersharing institutions were collapsed earlier this year by the DUP in protest against the post-Brexit Northern Ireland Protocol.
Sinn Fein Stormont leader Michelle O’Neill added: “It is too little, too late.
Our engagement with the Government both in Westminster and through Stormont departments is ensuring Northern Ireland households will get help this winter
Sammy Wilson, DUP
“We find ourselves in a scenario where we don’t have an executive up and running, we have announcements being made, and we still do not have one penny in the pockets of people in the north.”
But Mr Wilson said: “Over the last few weeks Sinn Fein and others have, broken-record like, been telling Northern Ireland homeowners that they will not qualify for energy supports because the executive is not fully functioning.
“This has been proved to be a lie.
“Whilst the Sinn Fein Finance Minister was whinging, the DUP has been working.
“Our engagement with the Government both in Westminster and through Stormont departments is ensuring Northern Ireland households will get help this winter.”
Business Secretary Jacob Rees-Mogg announced the energy price cap for homes in Northern Ireland on Wednesday.
He said households in Northern Ireland will be offered the same level of gas and electricity bill support as an equivalent scheme in Great Britain.
The announcement follows the launch of the Energy Price Guarantee in the rest of the UK, under which a typical household will pay on average £2,500 a year on their energy bill for the next two years from October 1.
The scheme limits the price suppliers can charge customers for units of gas and electricity.
The Government said the scheme will work through electricity and gas bills.
Energy suppliers will reduce bills by a unit price reduction of up to 17p/kWh for electricity and 4.2p/kWh for gas.
It has also said it will provide an additional payment of £100 to households who are not able to receive support through the price cap, such as those who use home heating oil.
The Government said there is no need for householders to take any action to receive the support.
It said the scheme will take effect from November, but it will ensure households receive the same benefit overall as those in Great Britain by backdating support for October bills through bills from November.
Northern Ireland is in a separate energy market from the rest of the UK but the Government has stressed people who live in the region will receive “equivalent support”.
Households will also receive a £400 discount on bills through the Northern Ireland Energy Bills Support Scheme, although no timescale has yet been given on when this will be made available.
The Government has also announced plans to introduce a cap on wholesale energy bills for businesses in the rest of the UK from October, and said a parallel scheme will be established in Northern Ireland.
The plan will see energy bills for businesses cut by around half their expected level this winter, although it is not yet clear when this relief will be available for firms in Northern Ireland.
Hospitals, schools, charities and other settings such as community halls and churches will also get help.
But hospitality chiefs said firms in Northern Ireland need “urgent clarity” on how the business relief scheme will operate in the region.
Colin Neill, chief executive of Hospitality Ulster, said: “It is simply unacceptable that Northern Ireland businesses do not have any detail on how support will be provided.
“We need urgent clarity on how these measures will be carried forward.”
Retail NI chief executive Glyn Roberts said: “Given the crippling financial difficulties that local independent retailers and other small businesses are experiencing, it is hugely disappointing that more clarity was not provided on the energy cap.
“We have been given no timelines on how the energy cap will apply to Northern Ireland business owners.
“This is unacceptable and our members deserve better.”