Earlier this month Lakhvir Singh and Sumit Sehdev – who have lived in Scotland for more than 10 years – were detained in a van on Kenmure Street for more than eight hours during an attempt by the Home Office to deport them.
Hundreds of residents gathered in protest and blocked the van from moving – with one man even crawling under the vehicle.
Challenged on her response to the scenes, the Home Secretary refused to change approach.
Appearing at a Bright Blue question and answer session, she said: “We will continue to do that, that is effectively what the British public have voted for, what they want.
“Actually it’s part of my legal duty as well and responsibility in terms of not just immigration enforcement but removing those with no legal right to be here.”
It came during a speech that also saw Ms Patel vote to fix the UK's "broken" immigration system.
She said: “They want a new system that works for the law-abiding majority and against those who hope to abuse our hospitality and generous spirit
“The immigration system is broken, but this country isn’t. We can’t fix the system overnight, but we will fix it.
“We have to make sure the system reflects the values and wishes of the vast majority of Britons of all colours and creeds.
“They simply want an approach to immigration that is fair but firm.”
Ms Patel also claimed public frustration over immigration led to the Brexit result, and claimed that along with the 2019 general election result was a mandate for "wholesale reform".
The senior UK Government Cabinet minister also insisted both she and the Prime Minister were both pro-immigration.
She added: "People across the country do not want their communities and way of life to be changed beyond recognition - and yet acknowledging this is not to be anti-immigration.
"Neither I, the PM, or our great country are anti-immigration. And to those who say that I am - they are wrong."
The SNP’s Immigration spokesperson Anne McLaughlin MP accused the Home Secretary of ignoring the fact that the her own party has been in government for 11 years.
She said: “These comments from the Home Secretary show, once again, just how out of touch the Tory government is with the people of Scotland.
“Scotland absolutely did not vote for these cruel immigration raids or any of the other toxic Tory migration policies. Nor did we vote for the Tory government or their hard Brexit that is making the UK more isolationist as the weeks go on.
“Indeed, the people of Glasgow and elsewhere in Scotland have made it abundantly clear that they will not stand by and let the Home Office ramp up these inhumane raids.
"We have made it clear we want a humane migration and asylum system that works for Scotland based on fairness, dignity and respect. Priti Patel’s speech today made clear that Scotland isn’t going to get that.”