The Home Secretary faced a backlash in parliament after it was announced that the number of lone child refugees coming to the UK will be capped.
Amber Rudd insisted that the move to cap the scheme to just 350 children, far fewer than the 3,000 originally expected, closed to avoid encouraging people-traffickers.
Labour MP Yvette Cooper told Mrs Rudd that by closing the scheme, they are "turning our backs once again".
Cooper, who chairs the Home Affairs Select Committee, said thousands of child refugees are languishing in camps in Greece and Italy, desperate for help and at risk of abuse, exploitation and modern slavery.
Addressing the Home Secretary directly, she said: "Britain can do better than this. Will she accept that and reinstate the Dubs programme now?"
"How does she live with herself?" Abbott said of Rudd. "Leaving thousands of children subject to disease, people trafficking, squalor and hopelessness."
Labour's Lord Dubs, who spearheaded the amendment, said he was puzzled by the claim and accused ministers of breaching their own commitments by "arbitrarily closing down" the scheme.
Responding to the Commons, Rudd said: "I am clear that when working with my French counterparts, they do not want us to indefinitely continue to accept children under the Dubs Amendment because they specify, and I agree with them, that it acts as a draw. It acts as a pull.
"It encourages the people-traffickers."
She also suggested that local authority funding had come into the equation when deciding how many child refugees would be settled under the programme.
She insisted that the UK is concentrating its efforts on providing aid and resettlement to vulnerable people in crisis-hit regions such as Syria.
Rudd said: "The UK has a strong reputation in Europe and internationally for looking after the most vulnerable. That will continue."
The Archbishop of Canterbury, Justin Welby said he was "saddened and shocked" to learn of the Government's decision to stop the scheme.
"Our country has a great history of welcoming those in need, particularly the most vulnerable, such as unaccompanied children," he said.
"Refugees, like all people, are treasured human beings made in the image of God who deserve safety, freedom and the opportunity to flourish."
He added: "We must resist and turn back the worrying trends we are seeing around the world, towards seeing the movement of desperate people as more of a threat to identity and security than an opportunity to do our duty.
"We cannot withdraw from our long and proud history of helping the most vulnerable."