Former Secretary of State Peter Hain has said he believes Julian Smith acted honourably in his pledges to the DUP and Sinn Fein over funding for the new Executive.
Sinn Fein Finance Minister Conor Murphy has said that the extra £1bn is inadequate and doesn't address Northern Ireland's health and education crisis.
The DUP and Sinn Fein expected significantly more funding from the Government following their deal to restore power-sharing last week, and they have faced criticism for not nailing a concrete commitment down in advance of signing up to the agreement.
Mr Hain last night told the Belfast Telegraph: "It is crucial when you are negotiating an agreement to tie up all the ends, to cross all the 'T's and dot the 'I's especially on funding.
"I believe the Secretary of State acted honourably and determinedly but that the Treasury retrospectively got its sticky paws onto the detail."
Addressing the House of Commons yesterday, Mr Smith rejected claims from Labour Shadow Secretary of State Tony Lloyd that the Government was "penny-pinching" following the deal.
"This is the best financial deal of any Northern Ireland talks settlement - £2bn," Mr Smith responded.
"This is an injection for this talks process, £1bn of new money, £1bn of Barnett-based funding up front, a guarantee.
"We then have the annual budget in March, the UK budget, and we have a deal for Brexit. So, the key task for this executive now is to focus on its priorities."
Mr Smith said the parties have agreed to publish the "fuller details of an agreed programme for government" within a fortnight of the restoration of the institutions.
"This Government stands ready over the coming months and years to work with the Executive, we really want to support it, but £2bn of money now is an extremely good start and I'm confident that is the basis for a strong future for Northern Ireland," he added.
Mr Smith said he was "slightly disappointed" that the parties had ruled out introducing water charges here.
"The Executive needs to look at its own revenue raising measures as well as coming to the UK Exchequer for cash," he said.
On the New Decade, New Approach deal, Mr Lloyd said: "The monies that the Government has so far made available simply will not be adequate for this ambitious document.
"What we cannot now do is see this process frustrated by a penny-pinching attitude by the Chancellor and a Prime Minister that will not accept the consequences.
"Secretary of State, I have to say directly to you - you've got to do better, you've got to go back to other government ministers and say we now need to see the resources made available."
Finance Minister Conor Murphy described the Government's package as an act of bad faith. He told the BBC that the government had "stepped back from its financial commitment" and that it "isn't acceptable".
He stated: "It wouldn't be acceptable if Sinn Féin, the DUP or any of the other parties said: 'We've made a political agreement - we're not going to do that, so you'll just have to get on with it anyway'. (The deal) does nothing to allow us to transform public services, it really keeps us in the austerity trap that we've been in for nine years."
Former Ulster Unionist leader Mike Nesbitt said it was hard not to view the government's actions on money as payback.
"Payback from the Conservative Party to the DUP for the way they treated them when they had the balance of power at Westminster, and also payback from the Treasury, who I think are sick of the kind of fill-your-boots attitude that some people here demonstrate when it comes to Treasury money outside of the bloc grant."
He said the UUP and the other smaller parties were excluded from the last two days of Stormont talks and did not know what was pledged around the financial package.
The Strangford MLA said the money would have to be used effectively and to maximum effect.
DUP MP Sir Jeffrey Donaldson said that if the deal was to work then "the resources need to be there in order to assure sustainability".
SDLP leader Colum Eastwood said: "There's lots of commitments in this deal and there is a gap between the commitments and the financial package offered."
TUV leader Jim Allister said that "extravagant" Irish language funding should be redirected to health.
Rounding on Sinn Fein and the DUP, he said: "With the Executive parties having spectacularly bungled the pre-agreement negotiations by failing to nail down the money issue, it would be absurd to squander still-scarce resources on vanity projects like needless Irish language infrastructure and enhancement.
"Where is the money going to come from for all the extravagant provision that is planned, but by having less money for real needs in health and education?
"In these circumstances, money intended for an Irish language commissioner and one in the Ulster Scots field, along with their teams of staff etc, would be far better spent on more nurses and doctors. But, no, for some the Irish language is more important," Mr Allister added.