Mario Balotelli's second-half winner denied England despite a spirited performance from Hodgson's young side. Their game against Uruguay -- who also lost on Saturday -- in Sao Paulo next Thursday is now effectively a knock-out tie for both teams.
"We were hoping for a perfect start, but we don't live in a perfect world," Hodgson told the BBC.
"I thought we played so well in the second half. I thought we would get back into it and maybe go on to win it because it was a quite dominant second-half performance. The positive we can take is that is the best I have seen the team play in my time with them and it is very good to know that we have players who will make us a much better team moving forward.
"I suppose you have to bite the bullet as we were up against a very good team. We are a very positive team. We are not the sort of team to sit back and unfortunately it left one or two opportunities for Italy to get the ball in.
"We had several situations near the end where we were desperate for that goal and we got into good crossing situations, good shooting positions and we didn't take advantage of it. I have to say we are a young team and we will improve moving forward.
"I thought Raheem Sterling was very dangerous throughout the game. [Daniel] Sturridge was excellent, Danny Welbeck had some good moments and Steven Gerrard and Jordan Henderson did everything expected of them.
"It's very tough to accept that we have lost the game, but the performance gives us great confidence going forward. We can do well against Uruguay and Costa Rica. I have great confidence that we can qualify."
England captain Gerrard also tried to find a silver lining in his side's loss, and suggested the attacking ambition on show at the Arena da Amazionia was an improvement on their last major tournament two years ago.
"Italy are a good team and we knew what they were going to have, how they were going to play," Gerrard said. "It's disappointing because we put so much into it and we come away with nothing.
"We got criticised two years ago [at Euro 2012 against Italy] for sitting back and being a bit toothless really, but anyone who saw that game could see we were trying to be creative. We pushed and pushed and we give everything we got. We are unlucky not to get something out of it.
"The chances were there, we created them. Maybe we have to look at finishing a few more of those chances off, but we can't point any fingers because everyone gave everything they have got.
"They caused us many problems down the left side in the first half, but we changed it in the second half and played most of the game in their half in the second half.
"No matter what the result was tonight, we were still going to have to beat Uruguay, but this makes it a little more difficult. We are not out of this group yet."