His comments come as Syria marked the seventh anniversary on Thursday of the popular uprising that sparked the country's vicious war.
Half a million Syrians have been killed and 6.1 million have been internally displaced, according to the United Nations.
Of Syria's estimated 10 million children, 8.6 million are in dire need of assistance, and nearly 6 million children are displaced or living as refugees.
Fr Nadim Nassar told Premier the international community's intervention has played a role in Syria's civil war.
"I'm not saying in anyway the international community should step back and leave Syria after such enormous involvement and engagement in the war of Syria. After the destruction, how can they step back?
"They shouldn't have engaged in the war from the beginning."
The US started arming and providing military assistance in 2014 for anti-President Bashar al-Assad rebel groups who were waging war against ISIS. They have also begun working with Syrian Kurds, who are also fighting against ISIS.
However, Syrian ally Russia has helped Mr Assad's regime, and Iran has provided assistance with troops and money.
Since August 2011, Britain, along with the US, France and some Arab states, has insisted that the Syrian president must step down.
While Fr Nassar criticised the numerous international forces having a role to play in the war, he said the Church needed to do more to try and end the violence.
He explained: "Unfortunately, I'm heartbroken to say... the international community is not on the right way to tackle the problem in Syria. People don't want to talk about it any longer because they look and they see such a huge disaster - even the Church.
"The Church is only helping in a humanitarian way but it's not enough. I challenge the leadership of the Church east and west... where are we? Where are the leaders of the Church to stand up and shout and scream in the faces of the politicians and say 'enough, stop the blood and stop this senseless war'.
"Unfortunately the position of the Church is appalling and it is shameful."
Dr Harry Hagopian, an expert on the Middle East who has travelled extensively in the region, said the conflict has escalated to an international war.
He told Premier's News Hour: "This has become a regional and an international conflict, and what really needs to happen is for the key decision-makers - Russia and the United States - to come together and say 'let's stop playing proxy politics'".
Calling for a complete cessation of the fighting, Christian Aid warned the situation in Syria has deteriorated with each passing year of the war.
Speaking to Premier from Lebanon, a regional advocacy officer for the charity, Máiréad Collins, said: "All we've seen every year is that the conflict has worsened and that the situation for civilians - both inside Syria and the refugees beyond its borders - has gotten worse every single year."
The Catholic charity, Cafod, urged Christians to pray that all sides of the conflict would come together to negotiate through the United Nations and that displaced families would be able to return to their homes.
Alan Thomlinson, CAFOD's Syria Crisis Programme Manager, told Premier: "This is a really shocking scale of displacement and of killings, and the destruction of homes, businesses, hospitals and schools.
"So, it really is a worry aspect to think this is now going into its eighth year."
Listen to Fr Nadim Nassar speaking with Premier's Eno Adeogun:
Listen to Premier's Alex Williams speaking with Dr Harry Hagopian:
Listen to Premier's Alex Williams speaking with Máiréad Collins at Christian Aid:
Listen to Premier's Alex Williams speaking with Alan Thomlinson at CAFOD:
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