The amendment, tabled by ex-Labour deputy leader Harriet Harman, was rejected by 332 MPs, while 290 voted for it.
Green Party co-leader Caroline Lucas said the outcome of the vote was "unforgivable", adding: "These are people's lives not commodities."
Harman had earlier said said: "It is unthinkable they would be deported, their families divided, because we have decided to leave the EU."
Theresa May has repeatedly refused to agree the future status of EU nationals until the rights of Britons living elsewhere in the bloc have also been secured.
Earlier today MPs were told "nothing will change" for any EU citizen living in Britain after Brexit without a vote in Parliament.
Securing the status of nationals from other countries remains a top priority for the Government once divorce talks formally begin, Amber Rudd insisted.
The Home Secretary wrote to reassure restive Tories ahead of a Commons vote on guaranteeing the rights of Europeans living in Britain to remain in the country.
But other leaders have refused to sign off a deal until Article 50, the formal process for quitting the EU, is triggered.
Tory MPs have raised concerns about the impact the uncertainty is having on the three million Europeans affected.
But Tory former minister Ed Vaizey, a would-be rebel, revealed he would not vote against the Government because he had been "deeply reassured" by the letter.
Ms Rudd wrote: "The Great Repeal Bill will not change our immigration system. This will be done through a separate Immigration Bill and subsequent secondary legislation so nothing will change for any EU citizen, whether already resident in the UK or moving from the EU, without Parliament's approval.
"I've always been clear that after we leave the European Union we will have an immigration system that supports our economy and protects our public services, and that should mean securing the rights of EU citizens already here, as well as establishing a new immigration system for new arrivals from the EU once we have left.
"But this isn't just about ensuring British businesses and our public sector have access to the right workers, we owe it to those many European citizens who have contributed so much to this country to resolve this issue as soon as possible and give them the security they need to continue to contribute to this country."
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