England finished bottom of Group D following two 2-1 defeats to Italy and Uruguay before a goalless draw with Costa Rica in what was the national side's worst World Cup since 1958.
Hodgson admitted he still feels "great disappointment" at England's early exit, but has merely put it down to misfortune.
England did not win a single game at the World Cup finals
"We lose the first game and in my opinion, a little bit unluckily," he told Sky Sports News. "We certainly played well enough and deserved more. Sadly we go into the second game and things are going okay and we got ourselves going.
"In the second-half, we see a bad goal conceded and somewhat a freakish goal [Luis Suárez's winner] and suddenly you've lost two and you're out of the competition before we've even started. It was a bitter blow and it's going to take more than a couple of months to come out of that.
"We have a lot of rebuilding to do not only of rebuilding our team but also rebuilding all the faith that people showed us. We felt that people were behind us and like ourselves believing this could be a good tournament for us but it turns out to be a bad tournament for you.
Luis Suárez's winner against England was dismissed as a "freakish" goal by Hodgson
"As a result, we have to look forward to 2016 and make certain that we don’t allow it to happen again and hope we don’t have the same lack of fortune as well that we perhaps suffered as well."
Hodgson added there is not a "vast amount of difference" in style between England and Germany, widely regarded as the most entertaining side not just in Brazil, but at the previous two World Cups in South African and in their homeland.
Joachim Löw's side scored 18 goals at the 2014 finals - which included a memorable 7-1 annihilation of Brazil in the semi-finals - yet Hodgson downplayed the growing chasm between England and the four-times World champions.
Germany won their fourth World Cup in Brazil
"I don’t believe in the nonsense spoken about the identity of certain countries and how they play," Hodgson said. "I don’t see the vast amount of difference between how we try and the way Germany try to play.
"Now there is a major difference between the 11 players in the German shirt and the 11 players in the England shirt. But if we are talking about how they attack and build up their attacks, or how they keep possession and seek for openings when they have got the ball, I don’t see a vast amount of difference in philosophy or style.
"And the same defensively. I don’t see what they are trying to do to keep compact to put pressure on the ball, to try and keep the team united close together, to block crosses. I don’t see the great difference in philosophy there either."
Hodgson has "half chosen" England's next captain following the international retirement of previous skipper Steven Gerrard, with Wayne Rooney expected to inherit the armband.