Wembley, the home of England's national soccer team, has previously lit up its iconic arch with the colours of Ukraine, Turkey and other countries in solidarity.
But it will not do so for England's international friendly versus Australia on Friday nor Tuesday's European Championship qualifier against Italy, media reports said.
"There are moments in history when the truth is one, sharp, clear. Such is the present time," IFA president Zuares said in a statement on Friday.
"More than 1,200 children, babies, women, men, old people, were slaughtered by a barbaric enemy, who committed crimes against humanity. The only sin of the victims was that they were Israelis.
"Those who are afraid to light up a stadium in memory of the murdered and for the sake of historical truth, for reasons that cannot be understood at all, and perhaps it is better not to even try, are in an even darker time than the one my country is currently in."
"When this happens by the FA of a nation that always knows how to be a moral lighthouse for the free world, it is (more) disappointing than ever," Zuares added.
"I tried to explain this to my colleagues in the English FA several times in the past days but they insist not to understand. Now they are the one who need to explain."
Hamas fighters killed 1,300 Israelis on Saturday. Israel has responded with the most intensive air strikes of its 75-year conflict with the Palestinians and Gaza authorities say 1,800 people have been killed.
The FA said in a statement on Thursday that flags and shirts showing support for victims of the Israeli-Palestinian conflict would not be allowed for England's next two games.
England and Australia would wear black armbands on Friday, the FA added, with a period of silence observed before kick-off.
The FA's arch decision was widely rebuked, including by the British government. Rabbi Alex Goldberg also stepped down as chair of the FA's Faith in Football network over the decision.
"We are sorry to hear of Rabbi Alex's decision to resign from his role in our Faith in Football group," an FA spokesperson said.
"Although this is an informal group that is not part of the FA's governance structure, we are grateful for the support he has provided over the years.
"It is also important to clarify that our decision not to allow Israeli or Palestine flags into Wembley Stadium was made at the direct request of senior members of the Jewish community."
