"This 1 millionth child refugee is not just another number," Lake said Friday in a release. "This is a real child ripped from home, maybe even from a family, facing horrors we can only begin to comprehend."
"We must all share the shame," said Lake, "because while we work to alleviate the suffering of those affected by this crisis, the global community has failed in its responsibility to this child. We should stop and ask ourselves how, in all conscience, we can continue to fail the children of Syria."
Young people in Syria are losing their homes, family members and futures, said Antonio Guterres, an official with the U.N. High Commissioner of Refugees.
Children make up half of all refugees from the Syria conflict, U.N. children and refugee agencies said. Most have fled to Lebanon, Jordan, Turkey, Iraq and Egypt, but data indicated Syrians increasingly were heading to North Africa and Europe.
Latest figures indicate more than 768,000 Syrian child refugees are less than 11 years of age.
"What is at stake is nothing less than the survival and well-being of a generation of innocents," Guterres said, adding, "Even after they have crossed a border to safety, they are traumatized, depressed and in need of a reason for hope."
UNHCR and UNICEF estimated more than 2 million children have been displaced internally within Syria.
The human rights organization said 7,000 children have been killed during the conflict that began in March 2011.