The UK Government said it respects "the spirit and the letter of the devolution settlement" as it presses ahead with Brexit without consent from the devolved administrations.
In letters sent to Scottish and Welsh ministers addressing their refusal to give legislative consent to Boris Johnson's deal, Brexit Secretary Steve Barclay said he recognised the "significant role" played by the legislative consent process.
He said the circumstances of the UK's departure from the EU are "specific, singular and exceptional" despite the Sewel Convention which says the UK Government should "not normally" press ahead without consent from devolved administrations.
It comes as the newly-restored Stormont Assembly in Belfast rejected the Government's EU withdrawal plan on Monday.
It was one of the first substantive acts of business since the assembly was restored earlier this month following the powersharing deal.
Welsh First Minister Mark Drakeford has urged assembly members to vote it down when it comes to the Senedd.
Under the devolution agreement, legislative consent is required for issues affecting devolved policy areas.
In practice, however, the UK Government is able to still proceed against the will of the Scottish, Welsh or Northern Irish administrations.
Writing to Scotland's Constitutional Relations Secretary Mike Russell, Mr Barclay said the UK Government would be ready to continue to engage with the Scottish Government as the Bill moves through its remaining stages at Westminster.
"I am disappointed that you do not feel in a position to recommend legislative consent to the Scottish Parliament," he wrote.
"I am also disappointed that the Scottish Parliament voted not to give consent, particularly with the Bill at such an early stage in its Parliamentary process.
"Despite the distance between our positions, I know we both recognise the enduring power and value of our historic relationship and also the important role of the legislative consent process - a principle to which the UK Government remains committed."
He added: "Over the years, this has helped ensure that UK-wide legislation both reflects the concerns of the Scottish Government and respects the devolution settlement.
"Both through significant engagement on the Bill and the changes we have made to accommodate your concerns, we have at every stage respected the spirit and the letter of the devolution settlement."
Mr Barclay added although the UK Government would be proceeding with the legislation despite not having the consent of the devolved administrations, it would "continued to work to address your concerns."
In his letter to Welsh Brexit Minister Jeremy Miles, Mr Barclay said: "I hope that you will revise your recommendation and support this Bill.
"It allows us to respect the result of the referendum, in which the people of Wales voted to leave the EU, to move on to focus on other priorities and at the same time bring the country together."
Mr Russell accused the UK Government of "ripping up the rules".
He said: "Throughout the Brexit process, the UK Government has ignored the wishes of the people of Scotland, votes in the Scottish Parliament and the views of the Scottish Government.
"The Tories have used Brexit to launch a power grab on Holyrood and Steve Barclay is now making it clear they are ripping up the rules that are meant to protect the Scottish Parliament so they can impose a hard Brexit."
He added: "By the end of tomorrow it is highly likely all three of the devolved legislatures in the UK will have refused consent to this disastrous Brexit Bill.
"If Boris Johnson presses ahead it will demonstrate once again his contempt for devolution and the idea of the UK as a partnership of equals.
"We strongly contest the assertions made in this letter and will reply to the UK Government in full."