Simon Johnson, chief executive of the Jewish Leadership Council and himself a former director of corporate affairs at the FA, strongly criticized Glenn's comment, saying the examples given were ill-judged and in poor taste. The Star of David, a symbol of Judaism, features on the Israeli flag which appears on national team kits and is displayed in stadiums.
"The problem we had with poppies is that for some reason a new person at Federation Internationale de Football Association seemed to think poppies were a political symbol and we fought hard against that notion and thankfully sense broke out", Glenn said.
Former Barcelona boss Guardiola has been a vocal proponent of independence in his home region and put forward his point of view in a news conference last week - likening the pin to those worn to raise awareness for charities and insisting his cause in this instance was humanitarian, not political.
A day earlier, he said: "Things like a poppy are OK but things that are going to be highly divisive are not".
Manchester City manager Pep Guardiola has accepted a Football Association (FA) charge for wearing a yellow ribbon, which the governing body deems to be a political symbol and in breach of its regulations.
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He said he watches all of today's great National Football League running backs but models his game after none of them. But the Giants and Colts badly need difference makers on offense and are thin in the backfield.
Glenn said the FA was "even-handedly" trying to apply the laws of the game.
As part of his apology, Glenn agreed with the JLC that the Star of David "is a hugely important symbol to Jewish people all over the world".
Glenn's comments came just days after it was announced that Prince William, the president of the FA, would be the first senior British royal to make an official visit to Israel, later this year. Poppies are not political symbols.
Glenn referenced the right-wing, euroskeptic U.K. Independence Party and the Islamic State group. "Should we have someone with a UKIP badge, someone with an ISIS badge?" he noted. "That's why you have to be pretty tough that local, regional, national party organizations can not use football shirts to represent them", Glenn said.