The former British politician, who now heads up the International Rescue Committee (IRC), said it will be much harder for the UK to maintain a global role after leaving the European Union, which has seen hundreds of thousands of men, women and children seeking refuge from the civil war in Syria.
With the UK poised to leave the bloc, Mr Milband said he hoped the Government's decision to renege on its promise to continue resettling vulnerable lone children in Europe was not a sign it was retreating from its humanitarian responsibilities when the international response to the crisis had already been "too little, too late".
Speaking from Iraq, he said: "I've seen the Government are saying they want to keep up the global role.
"But from my point of view it's obvious that leaving the EU makes it that much more difficult - many times more difficult - to maintain a global role, because the EU has been for 40 years a vehicle through which British values and British influence could be projected internationally, not least through the international aid and human budgets and policies that the EU has.
"However, the British people voted to leave and obviously it's very important that the drawbridge is not drawn up.
"I think the decision to abandon the previous Government's commitment to welcome 3,000 unaccompanied children is greatly to be deplored, and I hope it's not a signal that the rhetoric of global engagement is not going to be matched by policies to advance it."
Mr Miliband has spent the last week in Iraq and Lebanon, meeting people forced to flee Mosul as well as camps hosting refugees from neighbouring Syria.
The conflict, which will enter its seventh year next week, has seen more than half of Syria's population displaced, the charity estimates.
Mr Miliband condemned the inadequate support the states surrounding Syria were receiving despite their populations swelling, and refugees facing appalling conditions being driven to make the "deadly trek" to Europe.
The response to the conflict could be described as an "episode of international heroism on the one hand and international inadequacy on the other", he said.