The party’s Westminster leader Ian Blackford said leaving the blocs would “devastate our economy and cost jobs” as he urged the Prime Minister to secure a deal.
But Mrs May said Mr Blackford “continues to bark up the wrong tree”.
During PMQs, Mr Blackford said: “The clock is ticking and we need a deal that keeps us in the single market and the customs union - to do otherwise will devastate our economy and cost jobs.
“Will the Prime Minister recognise that such a deal will resolve the Irish border question and protect jobs throughout the UK - anything less will be a failure of leadership.
Mrs May replied: “We are leaving the European Union, that means we will be leaving the single market and leaving the customs union ... and we ensure that we can do trade deals around the rest of the world.”
Mr Blackford claimed the DUP had been given a veto over Brexit, and asked if Mrs May was a Prime Minister “in office but not in power”.
He said: “So now we know that the deal that was done with the DUP to keep the Prime Minister in office gave the DUP a veto over Brexit.
“It is embarrassing that it was being briefed on Monday morning that the Prime Minister had a deal, only to take this off the table after a call with the DUP.
“Is this a Prime Minister who is in office but not in power?”
Mrs May said the Government was working for a deal that would “work for the whole of the United Kingdom”.
“There are particular circumstances for Northern Ireland because it is the one part of the United Kingdom that shares a land border with a country that will be remaining in the European Union.
“But as we look ahead and during the negotiations, as (Mr Blackford) will know, we are consulting and talking with all parts of the United Kingdom - with the Welsh government and the Scottish government - and we want to ensure that we get the right deal for the UK.
“And that’s the deal that I’ve set out: we will be leaving the European Union, we will be leaving the single market, we will be leaving the customs union but we will ensure that we get that good trade deal for the future.”