In a published report to his party officers, Mr Robinson reiterated that all five Executive parties agreed for the talks to be set up to consider issues of parades, flags and the past and chose Dr Richard Haass as the independent chair of these discussions.
He stressed that both he and deputy First Minister Martin McGuinness stated that "failure would not be a failure on the part of Dr Haass but to our local parties".
"While the final Haass document contains many propositions that the DUP can support and endorse, there remain others that would neither be an improvement nor workable and would not help in resolving the problems they were crafted to solve," he commented.
"We are satisfied that the broad architecture is capable of housing long-term workable arrangements, yet the detailed components as drafted which would determine how those structures would operate need much more work before they could function in the best interests of the community."
The DUP leader said he agreed with Dr Haass in that the outstanding issues "need to be tackled now rather than later".
"Unquestionably the work Dr Haass and his team have undertaken has narrowed the gap in a number of areas and our understanding of each party's position will aid future negotiations," he added.
Any party's failure to agree to a proposal also reveals the failure of other parties to find a proposal capable of reaching wider agreement.
Peter Robinson, DUP leader
At a press briefing Mr Robinson said his party officers had supported his recommendations to support an ongoing process and agree to set up an all-party Working Group.
His response follows the Ulster Unionist Party's rejection of the Haass proposals on Monday night.
Following a meeting of the party's ruling executive, the UUP said the proposals were "not viable and therefore unacceptable" and called on OFMDFM to "sort out the mess".
The announcement came after party leader Mike Nesbitt said he was "optimistic" of an agreement during the final stages of the talks in December.
Reacting, Alliance Party MLA Stephen Farry said the rejection of the proposals showed "disdain for the Northern Ireland people".
"Mike Nesbitt himself has some explaining to do. Less than a week ago, he was clearly indicating his intention that the UUP would be giving a positive response," he commented.
"So either he was being disingenuous or he is a willing captive of the extreme elements in our society that are simply not prepared to compromise for the greater good.
"In particular, the UUP must now explain where it stands on the rule of law and a shared society.
Alliance recognises that while the outcome from the Haass talks is not perfect, major elements of that package do have the potential to transform this society for the better.
Stephen Farry, Alliance
Mr Farry added: "All political parties have a duty to recognise the imperative of making progress and to sit down with each other over the coming weeks to see what can be put in place, with dealing with our past seemingly providing the immediate opportunities."
SDLP West Belfast MLA Alex Attwood, who was part of his party's negotiating team, said the needs of victims "must prevail" and the UUP's rejection of the proposal represented a Pontius Pilate moment for the party.
"Washing their hands of the proposals is not an act of leadership. To then suggest handing it all over to FM and dFM, where issues and politics are so stuck, is plain bad judgement," he said.
"To move Haass forward needs action by the two governments and the five parties."
He continued: "The two governments have made it clear, for example, that they accept Haass on the past.
"This should be an impetus for the two governments and five parties together to decisively take forward addressing the past.
The SDLP again calls for a five party working group to be established. Not another talking shop but an implementation and legislation group working to tight timelines in order to create certainty, remove doubt, and build hope.
Alex Attwood, SDLP
Former US diplomat Dr Richard Haass, along with his co-chair and international affairs expert, Professor Megan O'Sullivan, were tasked with finding a consensus on the three contentious issues of the past, parades and flags by the First and Deputy First Ministers.
The group met with the main political parties, victims' groups, campaigners and members of the public to try to find a consensus on the issues.
Despite marathon sessions of talks, seven draft sets of proposals and a failure to meet the Christmas deadline the process ended without an agreement being reached.
Following the process, Dr Haass presented his final proposals to the Office of First and Deputy First Minister and urged the Executive and the parties to build on the work of his project.
Dr Haass has published a two-page factsheet outlining his main proposals.
He said his draft agreement: "Would leave the people of NI considerably better off than they are today by tackling the difficult issues that continue to divide society."
Sinn Féin deputy First Minister Martin McGuinness, whose party was the first to support the draft proposals has claimed that "rejectionist elements" of the Orange Order and "extreme loyalism" were allowed to set the agenda by the DUP and the UUP.
Gerry Kelly of Sinn Féin on Tuesday added that people "deserve much better political leadership than being given by the unionist parties".
The North Belfast MLA went on: "Both parties were quick to dismiss the allegation that they are being led by the nose by the Orange Order and extreme loyalism.
"Yet it is difficult to come to any other conclusion as events unfold.
"This process like every other negotiation requires political leadership and political courage. Negotiated documents are by their nature compromises. Unionist leaders are failing the test of political leadership and ignoring the vast majority of people here who want to see agreement and want to see politicians making deals and honouring them."