Sunak struck a new deal on Monday to ease trade restrictions in the British-run province, partially unwinding an earlier arrangement by Johnson that introduced checks and paperwork on goods arriving from the rest of Britain.
Johnson, who was forced to step down as prime minister last year after a series of scandals, said he had been at fault for not realising just how "onerous" the checks would be.
He said he would understand if politicians in the province choose to back the new deal in an effort to resume the region's power-sharing assembly.
But Johnson, whose allies blame Sunak for helping to oust him as prime minister, said the new agreement did not go far enough and he would struggle to vote for it.
"I'm going to find it very difficult to vote for something like this myself because I believe that we should have done something different," Johnson said, breaking his silence on the agreement in a speech at the Global Soft Power Summit 2023.
"We must be clear about what is really going on here. This is not about the UK taking back control ... This is the EU graciously unbending to allow us to do what we want in our own country. Not by our laws, but by theirs."
Asked about Johnson's comments, the prime minister's spokesman said while Sunak "understands that people will have questions and opinions" he believes it is the best deal for the people of Northern Ireland.
Parliament is due to vote on the deal. While it should pass with the support of the opposition Labour Party, a rebellion in Sunak and Johnson's Conservative Party could revive the deep ideological divisions that have at times paralysed the government since the vote to leave the EU in 2016.
Sterling fell against the U.S. dollar and euro after Johnson's comments, extending losses from earlier in the day.
Sunak had hailed the agreement as historic, one that enables Britain to move on from the Brexit rows of recent years and reset its relationship both with the EU and the United States after U.S. President Joe Biden voiced concern about the political strains developing in Northern Ireland.
Its success is likely to hinge on whether it convinces the Democratic Unionist Party (DUP) to end its boycott of power-sharing arrangements in Northern Ireland. These arrangements were central to the 1998 peace deal known as the Good Friday Agreement which mostly ended three decades of violence there.
Johnson said he hoped the province's largest unionist party, the DUP, could reconcile itself to the proposal so it can return to the power-sharing assembly in Stormont. The DUP has yet to say how it will vote.
The 58-year-old Johnson, the face of the Brexit campaign in Britain who clashed with Brussels for years over the nature of the UK's departure, has argued that an exit from the EU only makes sense if Britain radically changes its economy.
Sunak's deal defeated that aim, he said, because it allowed the EU to act as a "drag anchor" on Britain's ability to diverge from the bloc's rules and regulations.
"There's no point in Brexit unless you do things differently," Johnson said.
Any diversion has been made harder by the need for the border between Northern Ireland and EU-member Ireland to remain open to maintain the peace deal. Johnson had advocated a more hardline stance, sticking to a bill he introduced that would all but rip up his original deal, the Northern Ireland protocol.
"Given that we have got rid of the bill I can see why so many people are attracted to accepting a compromise," he said.