The British government blames the FA - and not England's players - for their World Cup failure.
Ministers said the early exit from South Africa and past tournament flops were the fault of the FA rather than the players.
Sports Minister Hugh Robertson told the London Evening Standard: "The people who are ultimately responsible are the FA because as the sport's governing body, they are responsible for the England team.
"Once the dust has settled, the FA need to have a long, cold, hard, unemotional look at this and work out why a country that has the best professional league in the world woefully underperforms at World Cups."
He added: "The players need to get away and have a rest. This really is an issue for the FA."