"Significant numbers of Iraqi children have been traumatised by conflict and are considered easy prey for radicalisation," the anti-persecution charity, Release International (RI) reports.
Some Iraqis say life for believers was easier prior to the war and subsequent rise of so-called Islamic State (IS), when the country was led by Saddam Hussein, RI said.
The invasion led to 179 British personal deaths, while many thousands of Iraqi civilians died.
It is believed a break down of law and order has fuelled an exodus with 80-per-cent of Christians in Iraq fleeing the country, leaving only a "dwindling" community of around 250k believers.
Commenting in light of the publication of the Chilcott Report on Wednesday which investigated the Iraq War, RI's Chief Executive, Paul Robinson said: "The future looks bleak for Christians in Iraq as the Shia-Sunni sectarian conflict spreads across the Middle East. Christians, as ever, are caught in the crossfire."
Although it has been losing ground in recent months, IS has reportedly been demolishing churches, confiscating Christian-owned property and using female Christians as sex slaves.
Meanwhile, it emerged on Friday IS had claimed responsibility for a mortar attack on a Shia shrine in Baghdad which killed 30 people and wounded dozens more.
The'ar, who fled Baghdad with his family after extremists bombed his church - killing 58 people - told RI: "There is no hope.
"Since [the invasion in] 2003, we have all this bombing and fighting. We have no future. Our prayer is to leave this country, just to be human and to raise our kids with dignity."
IS suicide bombers are regular targeting Shia neighbourhoods in Baghdad, while there are fears in the semi-autonomous Sunni region of Kurdistan that Shia Iran might penetrate its borders.
One ray of light is said to be in Kurdistan - which has welcomed Christian refugees - where Muslim-background believers are "flourishing", though there are reports of land and homes being seized.