Israel has withdrawn its first United Nations draft resolution in nearly 30 years in the face of strong opposition.
Annan has criticised both the General Assembly and Israel
The Israeli draft, which called for the protection of Israeli children from terrorism, mirrored one on Palestinian children passed earlier this month.
But mostly Arab opponents of the text introduced changes Israel could not accept, ambassador Dan Gillerman said.
He said the UN was telling Israeli children "that your lives are worth less than Palestinian children".
"Perhaps someone can explain to me why the hundreds of Israeli children killed or maimed in brutal terrorist attacks deserve less sympathy and attention," the Israeli ambassador said.
Israel sees the UN - with its large Muslim contingent - as openly hostile.
Mr Gillerman said that as long as this continued no one should wonder why the credibility and relevance of the UN is questioned in the Middle East.
The General Assembly passes more than 20 resolutions criticising Israel each year, which Israel ignores. Its Third Committee approved the Arab resolution on 6 November.
UNGA resolutions are not binding, unlike Security Council measures.
Israel decided to introduce its own resolution, which seems closely based on an Egyptian one in defence of Palestinian children, after a suicide bomber killed 21 people in Haifa last month.
Four of the dead were children.
But a number of countries of the Non-Aligned Movement, led by Egypt, introduced amendments to the Israeli draft that Israel could not accept.
They removed references to "Israeli children" and replaced them with more general language about "children of the Middle East".
The US blocks anti-Israel resolutions in the Security Council
They also added references to Israeli "military assaults" and "excessive use of force".
"The changes proposed are not amendments, but they are shameless attempts to deny Israeli children the attention that Palestinian children have already received," Ambassador Gillerman reportedly said.
The Palestinian representative at the UN, Nasser al-Kidwa, said the draft never had a chance of success.
He suggested Israel was acting "Don Quixote style, to create battles and then scream foul".
He said Israel had abused the word "children to achieve political goals".
But Ambassador Gillerman said the UN's failure to back the draft showed it as "an unreliable and biased body with no international integrity".
The UN has not always been so critical of Israel - in fact, the country was created by a UN vote in 1947.
The UN moved to partition the British mandate of Palestine into two states, one Jewish and one Arab.
The Arab part was divided among Israel, Egypt and Jordan in the wake of war in the region in 1948.
A solid anti-Israel bloc emerged at the UN after Israel's victory in the 1967 war left it in control of swathes of Arab territory.
The United States blocks anti-Israel resolutions at the Security Council if Washington does not consider them "balanced".
UN Secretary General Kofi Annan has criticised both the General Assembly's anti-Israel resolutions and the present Israeli Government.