England lost their opening two games to Italy and Uruguay and their faint hopes of avoiding elimination at the group stage for the first time since 1958 ended when Costa Rica beat Italy on Friday in Group D.
Hodgson, 66, who steered Switzerland into the last 16 of the World Cup in the United States in 1994, told reporters his team could not have prepared any better or done a lot more than they did in the two matches.
"At the moment we just have to suck on this very bitter pill - that our hopes and dreams have floundered here because we were unable to win two very tough games," he said.
"I don't have regrets. I don't think the team let anyone down, I think everyone worked very hard and we could not have done any better.
"We have a very strong basis for a team, it's very young."
While England have turned in disappointing performances in Brazil, those players will be a solid foundation as they gain experience with their club teams ahead of the 2016 European Championship, Hodgson added.
"Within the space of two years the youngsters in this team will be playing regularly in the Premier League and they will get better and stronger as an England team," he said.
"I have never doubted this team as it moves forward - not just to the Euros in 2016 but on from there. They will become stronger and better."
Hodgson also rejected criticism that England should have paid more attention to striker Luis Suarez in the Uruguay defeat and playmaker Andrea Pirlo when they faced Italy.
Suarez scored both goals in Uruguay's 2-1 win while Pirlo pulled the strings in midfield to orchestrate Italy's victory by the same scoreline.
"Suarez, by his standards, was fairly quiet for long periods of time due to the fact that he was maybe not 100 percent fit against us," he said.
"Personally, in the two lots of 90 minutes I think we couldn't have done much more against those two players."
Hodgson, who has coached clubs and national teams around the world, also said his energy and appetite for the game has not been affected by the failure in Brazil.
England play Costa Rica on Tuesday in Belo Horizonte, giving Hodgson and his squad a final opportunity to notch a win at the tournament before heading home.
"My enthusiasm for football is not likely to wane and my enthusiasm for working with these players is not likely to wane either," said Hodgson.
"We have a lot of exciting young players. Wayne Rooney is still only 28 years of age.
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- Costa Rica
- Luis Suarez
- England team