The complaint centres around allegations that Greek officials sold some of their ticket allocation to England fans for personal profit, causing security problems during the game.
Paul Newman, the FA spokesman said: "We have sent a letter of complaint to FIFA expressing concern about the Greek Football Association's ticket distribution. The matter is now in FIFA's hands. Suffice to say that we gave the Greeks 1,400 tickets for the match and we have heard various stories about how they were distributed."
A security source added: "Greek officials were observed selling tickets to England fans in Greece's hotel last week. The result was that England supporters entered areas of the stadium reserved for Greece fans and we had to take their flags away from them. Even so, these supporters were still easily identifiable as England fans and there could have been trouble if the atmosphere had turned ugly."
