England were eliminated at the group stage of the Fifa World Cup for the first time since 1958 as Italy lost 1-0 to Costa Rica in Recife.
They needed Italy to win both of their remaining games to stand a chance of reaching the last 16.
But Costa Rica’s defeat of the Azzurriended England’s involvement.
The England team watched Friday’s match from their hotel base in Rio.
Former England defender Rio Ferdinandbelieves a lack of experience cost Hodgson’s side, but thinks the tournament will be important for the development of their young players.
He said: “Maybe England were a bit naive in situations. In the game against Uruguay, for instance, when they got back to 1-1 they had a chance to get a point and everything would have been down to the final game.
“But the players can take experience from the tournament. It is valuable, not just playing minutes but being around the hotel, how you prepare yourself, what it means to go to a World Cup and feeling that pressure.”
Hodgson had picked a squad with an emphasis on youth, and was hopeful they would be able to progress out of a tough group.
Costa Rica were supposed to be the weakest team in a pool containing three former World Cup winners, but the Central American side were the first to secure their place in the last 16.
Despite England’s campaign starting with a 2-1 defeat by Italy, a promising performance gave them confidence for Thursday’s game against Uruguay, who lost their opening match to Costa Rica.
However, Luis Suarez’s two goals gave Uruguay a 2-1 victory which left Hodgson’s men relying on other results.
“We are supportive of Roy – he came to do a four-year cycle. I already see people asking the question, ‘Will he stay?’ The answer is yes,” said Dyke.
“He came to do a four-year cycle leading up to Euro 2016.”
Former England winger Chris Waddle cited a lack of quality coaching in the country as a reason for the national side’s failure.
Waddle, part of the England side beaten on penalties by West Germany in the semi-finals of the 1990 World Cup, told BBC Radio 5 live: “The Premier League is different to any league the world and that is our big problem.
“It’s frustrating, because we have everything we need – money, facilities – but it comes down to coaching, and we have to get something right about producing players.
“The Premier League is a great advert for our football but it does our national team no good whatsoever.”
England finish their campaign against Costa Rica on Tuesday.