The Foyle MLA has urged people to opt for candidates opposed to withdrawal from the EU during next month’s General Election.
The DUP believe British Prime Minister Boris Johnson’s proposed deal would create a regulatory border between the North of Ireland and the rest of the UK due to its mechanisms to protect all-Ireland trade.
Mr Eastwood told the Press Association: “It is unfortunate that people have followed them into that trap.
“They have done untold damage to the image of unionism right across the world and I think that is unfortunate.
“People should begin to understand that if you keep voting the way you have always voted you are going to get the same result.”
The SDLP has stood aside candidates in three constituencies – North Belfast, East Belfast and North Down – to give pro-Remain candidates the best chance of triumphing.
Their critics have accused them of sectarianism since their targets in each case are DUP candidates.
The number of votes the SDLP command in East Belfast and North Down is small.
Mr Eastwood said: “The calculation is simple, we want to take as many Brexiteers out of the UK Parliament as possible.”
The DUP’s deputy leader Nigel Dodds is defending his seat in North Belfast.
The SDLP stood aside for Mr Dodds’ Sinn Fein opponent, John Finucane, the son of murdered solicitor Pat Finucane.
Mr Eastwood admitted it was uncomfortable for his party not to be standing in any constituency, particularly given its criticism of Sinn Fein for not taking their seats, but said the SDLP had no prospect of winning North Belfast.
“In North Belfast it is an empty seat or Nigel Dodds – I prefer an empty seat.
“Nigel Dodds has been the architect of a bad Brexit and people understand that.”
The DUP has vetoed Theresa May and Boris Johnson’s proposed withdrawal deals.
Mr Eastwood said nobody could substantiate claims his party’s decision to step aside in key constituencies was sectarian.
He also countered unionist fears raised about the constitutional future but said the DUP’s support for Brexit made a united Ireland more likely.
The SDLP leader said: “The border won’t move one inch because of it.”
Abortion was recently legalised in Northern Ireland after MPs legislated for the move.It is an issue which has split nationalists and unionists.
Mr Eastwood said he did not support locking people up for having a termination but said the Stormont Assembly was the best place to deal with the issue.
“People have been lied to and people have used the issue for their own political purposes.
“Change is coming because of High Court cases.
“We can shape the change or let others shape it for us.”