The upper chamber of parliament defied the prime minister on Wednesday by voting 358 to 256 in favour of a Labour amendment calling for such rights to be safeguarded.
Lord Alton, a Christian and independent cross-bench peer who supported the amendment, told Premier: "I hope that the House of Commons will now reconsider this question of what we do about EU nationals who came to this country legally and who are entitled to live in our own land. Many have been settled here for many year."
Describing the result as "disappointing", ministers have suggested they will try to overturn the amendment when the Bill returns to the Commons on 13th and 14th March.
Lord Alton went on to say: "The government is entitled - and the House of Commons even more so - to get their way in the end but the House of Lords also has a specific duty to scrutinise legislation and to say where it thinks legislation has been got wrong by the House of Commons."
He was among 78 independent cross-bench peers and seven Conservative rebels who supported the amendment.
The Government argued while it wants to safeguard the future rights of EU citizens in the country, it must be able to secure reciprocal rights for British citizens living in other EU nations at the same time.
Explaining his decision, Lord Alton continued: "This isn't about the future and the future movement of people, it's not about holding up the Brexit Bill but it's about a specific question.
"I think the House of Lords is right to simply ask the Commons to think again on this particular question."
Click here to listen to Premier's Alex Williams speaking with Lord Alton: