"Our colleagues dedicated their lives to working for the children of Somalia. They are not victims. They and those who were wounded are heroes. We mourn their loss and hope for the full recovery of the injured," Lake said in a statement.
He said the organization's continuing work for the most vulnerable children and their families would be a "fitting tribute" to the victims of the attack.
"All of us at UNICEF are deeply saddened, and deeply angered," Lake said.
According to police officer Mohamed Abdi, cited by UNICEF, at least nine people died in the attack, with two Kenyans and seven Somali guards among them.
An al-Qaeda affiliate, al-Shabaab, is known to be operating in Somalia, occasionally staging attacks in the country. No one has yet claimed responsibility for the attack.
