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After the match the 66-year-old insisted he was not tempted to resign and Dyke has now revealed the Three Lions boss retains the backing of the FA.
"We're supportive of Roy Hodgson, we've asked him to stay as manager," he told Sky Sports News. "We were not humiliated [against Italy and Uruguay]. They were narrow defeats. We don't see any great value in changing Roy. He's done a good job.
"It's an approach over four years and we need to do better in the Euros [in 2016]."
When asked if England could still meet his target and win the 2022 World Cup, Dyke replied: "Yes I do actually, but I think it means lots of changes in English football."