"Cabinet expressed its strong disappointment at the defeats inflicted on the European Union withdrawal bill in the House of Lords, saying they risked tying the government's hands behind its back in negotiations with Brussels", May's spokesman told reporters.
It was seventh of nine defeats in the last two weeks for the government, which says the European Union withdrawal bill is purely a technical document to "copy and paste" European Union law into British law and guarantee a smooth Brexit.
He conceded the parliamentary arithmetic was hard in a hung parliament.
"Now the house of Lords are saying you've made the wrong decision, and we're going to do everything we can to overturn it".
Martin Callanan, the government's Brexit minister in the Lords, said during the debate: "I do not believe that it is in the best interests of the country to redefine the nature of our democracy in this way".
"What is important is that it keeps the government's hands open on negotiations with Brussels".
Key Brexiters want to drop one of the two options put forward by the government.
The UK and European Union have agreed there will be no hardening of the Irish border but are at odds on how to achieve that.
The EU's backstop proposal, which would mean Northern Ireland staying in the customs union and much of the single market, has been rejected by the UK.
"I don't think there is a customs union that could ever be acceptable", he said. "That is not what the public voted for".
"This is not. about creating a constitutional crisis, nor is it about asking the Commons [the lower house] to take on the negotiations.it is to ask the Commons and Parliament to decide whether the outcome of the negotiations is good enough", said Dianne Hayter, the opposition Labour Party's Brexit spokeswoman.
The government suffered an eighth defeat when lawmakers backed an amendment requiring ministers to seek parliamentary approval for their negotiating mandate in the next round of Brexit talks on Britain future relationship with the bloc.
The third defeat was led by the Labour peer Alf Dubs, who won backing for his amendment that would ensure child asylum seekers would be allowed to join family members in the United Kingdom after Brexit.
Former deputy prime minister Lord Heseltine and ex-ministers Lord Patten of Barnes and Lord Willetts were among 19 Tory rebels to support the cross-party amendment calling for Parliament to be given the decisive say on whether to accept the Brexit deal.