Nicola David was speaking after EU leaders agreed to give €1 billion to Lebanon, Jordan and Turkey to help them resettle refugees. Britain also pledged £100 million to the bordering countries.
Earlier in the week, EU countries agreed to take a quota of 120,000 refugees between them, however some Eastern European countries have resisted the quota claiming they cannot cope with more people coming.
Slovakia has launched a legal challenge against the quota. Britain has opted out, but previously pledged to take in 20,000 Syrian refugees.
Mrs David said World Food Programme vouchers given to refugees who chose not to stay in camps in Lebanon, Jordan and Turkey had run out, meaning they faced either starving or going back to conflict-ravaged Syria.
The expert also said that the money the EU offered was too little too late, adding that while Britain's previous pledge to take in 20,000 Syrian refugees was welcome, it was little in comparison to Jordan, which has taken in 80,000 refugees, and Lebanon, where 1 in 4 people is now a Syrian refugee.
She also said refugee camps also suffered from the cold and a lack of sewage systems.
Mrs David told Premier's News Hour: "People who've chosen not to go to the camps no longer WFP food vouchers... and so people are having to go back to Syria, now can you imagine? Choosing to go back into a conflict zone like Syria because it's start or face starvation and death.
"I'm always pleased to see that support's going to Syria, but I feel as though it's very late and we've ended up in quite a mess if perhaps we'd acted a bit sooner.
"We need to stand up as a nation, as Europe, and be counted, because if we don't we're going to have such a sense of shame.
"I'd like to see churches having a united response, I feel we don't hear enough from churches... It's time to show what we're made of, as a nation and also as a faith."
Meanwhile Christian Aid has welcomed the EU's €1bn, but added that the relief effort is "drastically underfunded", particularly with Winter approaching.
It also expressed "deep disappointment" that the British government has refused to take in any refugees who have already reached Europe.
Tom Viita, Christian Aid's senior political advisor, said: "Aid to Syria and neighbouring countries is currently less than 40 per cent of what is needed, so we welcome the EU decision to increase funding immediately, with more promised next year.
"The UK has played a major role in helping fund relief efforts in the Middle East, which is laudable, but its reluctance to accept any of those refugees who have recently arrived in Europe is deeply disappointing.
"The UK is now alone in the EU in taking such a hard-line stance.
"As well as helping in the Middle East, the UK must shoulder some of the responsibility of assisting those who have risked their lives to find sanctuary in Europe."
Listen to Premier's Hannah Tooley speaking with Nicola David on the News Hour:
