In letters sent to Scottish and Welsh ministers addressing their refusal to give legislative consent to Boris Johnson's Brexit deal, Secretary of State for Exiting the European Union Steve Barclay said he recognised the "significant role" played by the legislative consent process.
He said despite the Sewel Convention holding that the UK Government should "not normally" press ahead without legislative consent motions from devolved administrations, the circumstances of the UK's departure from the EU are "specific, singular and exceptional".
Members of the newly-restored Stormont Assembly in Belfast are also expected to reject the deal.
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."