Football Association chairman Greg Dyke said that the 66-year-old will continue in his role until Euro 2016, even though Hodgson's side recorded the earliest exit from the tournament by an England team in 56 years.
Hodgson told reporters: "My enthusiasm for football is not likely to wane and my enthusiasm for working with these players is not likely to wane either.
"I don't have any regrets and I don't think the team let anyone down. I think everyone worked very hard and I don't think we could have done any better.
"It's very hard to be happy when you lose, results colour everyone's judgement. We have played two experienced and strong teams, and on both occasions we have come second."
England face Costa Rica in their final game of the 2014 World Cup.