The critique is part of a new report called 'A Safe Haven?', which has been launched by 13 aid and refugee agencies including CAFOD and Christian Aid.
It says there has been a "lack of adequate response" from the UK and European governments to more than a million refugees and migrants who arrived in Europe in 2015.
That has "compounded the suffering and created a humanitarian crisis on Britain's doorstep", the report adds.
Anne Street, CAFOD's Head of Humanitarian Policy said: "It's not enough for the UK government to provide aid for refugees in countries like Lebanon and Jordan.
"The UK has an obligation to offer a safe haven, to take its fair share of refugees and do all it can to ensure protection for people on the move, whatever their legal status."
The report outlines key steps the UK must take to respond to the migrant crisis.
The Minister for Syrian Refugees, Richard Harrington, recently said in a speech to the United Nations: "For the UK's part, the Prime Minister announced that the UK will more than double our support to the Syria crisis to over £2.3 billion.
"The vast majority of this resource will be spent supporting refugees and displaced people in Syria and the region.
"We want to give refugees the chance to make a life close to their home.
"We believe that this is the most effective way of helping the large majority of the refugees and their host communities.
"Therefore, on top of our resettlement commitment of 20,000, the UK has committed to work with the UN High Commissioner for Refugees to lead a new initiative to resettle unaccompanied children from conflict regions, where it is in the children's best interests."
Listen to Premier's Aaron James speaking to Anne Street:
