Sinn Fein and SDLP parties furious at Brokenshire's EU stance
The DUP is urging the Secretary of State to stand firm on his declaration that Northern Ireland is unlikely to remain in the single market or customs union after Brexit.
Sinn Fein and the SDLP said James Brokenshire didn't represent the interests of the majority of people in Northern Ireland.
The Secretary of State was in Brussels to meet leading EU figures including chief Brexit negotiator Michel Barnier and agriculture commissioner Phil Hogan.
He updated them on Stormont's power-sharing crisis and highlighted the issues Brexit poses locally.
Mr Brokenshire said a bespoke solution for Northern Ireland was unlikely to see it remain in the single market or customs union.
"We joined the Common Market in 1973 as one United Kingdom and we will leave the European Union in 2019 as one United Kingdom," he said.
"As the Prime Minister has made clear, leaving the EU will mean that we leave both the single market and the customs union.
"I find it difficult to imagine how Northern Ireland could somehow remain in while the rest of the country leaves."
However, he pledged that the government was determined to find "bespoke solutions to Northern Ireland's unique circumstances, not least as the only part of the UK to share a land border with an EU member state".
He said: "We fully recognise the extent to which the Northern Ireland economy, while an integral part of the UK economy, is also fully integrated with that of Ireland, particularly in areas like the agri-food sector.
"We fully recognise the flow of traffic across the border on a daily basis for people going about their business - be it to work, study, shop or simply visit friends and relatives.
"And we fully recognise those ties of family and shared history that exist between people on the island of Ireland as well as between Ireland and Great Britain.
"All of this requires creative and imaginative thinking by the UK and Irish governments along with the EU."
DUP MEP Diane Dodds urged Mr Brokenshire to stand firm on Northern Ireland leaving the single market and the customs union and said there must be "no new border between Britain and ourselves".
She said: "The DUP will not countenance internal borders within the UK single market.
"The EU has said the outcome must uphold the Belfast Agreement but this must not give Brussels license to renegotiate the terms of cross-border relations to serve their own interests.
"Brussels has made a positive contribution to progress in Northern Ireland through consecutive PEACE programmes.
"However, its final act should not be to overreach into affairs over which it has no authority."
UUP MEP Jim Nicholson said he had a "useful, constructive meeting" with Mr Brokenshire and urged him "to keep coming back to Brussels to put the Northern Ireland view".
Mr Nicholson also expressed concern at the lack of a Stormont Executive voice in Brussels.
SDLP leader Colum Eastwood said: "The Secretary of State does not speak for the remain majority in Northern Ireland, his party has no representation and no mandate here.
"Yet the absence of an Executive and Assembly is allowing him to inherit the role as our voice and representative on Brexit.
"The imposition of direct rule will only make this situation worse."
Sinn Fein MEP Martina Anderson claimed it was hypocritical for Mr Brokenshire to talk about protecting Northern Ireland interests when "in reality his government's Brexit agenda can only damage those interests".
Alliance deputy leader Stephen Farry said full consideration should be given to "allowing Northern Ireland as a region to remain within the EU single market, alongside continuing to operate within the UK single market".