England were narrowly beaten by Italy on Saturday after goals from Claudio Marchisio and Mario Balotelli condemned Hodgson's men to a 2-1 defeat in Manaus.
Daniel Sturridge equalised eight minutes before half-time but England were unable to find a way back into the match after Balotelli nodded home in the 50th minute.
Speaking to BBC post-game, Hodgson said the performance gave him the belief that England can advance from the group, which also features Costa Rica and Uruguay.
"We were hoping for a perfect start, but we don't live in a perfect world," said Hodgson.
"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.
"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."
Hodgson added: "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."
Hodgson also leapt to the defence of under-fire forward Wayne Rooney, who was deployed on the left wing as Sturridge led the line for England.
Rooney set up England's equaliser, delivering an inch-perfect cross for Sturridge to slam home, but the Manchester United star, who squandered a golden opportunity to end his World Cup drought in the second half, was still criticised for his overall display.
"I think it is harsh to say he didn't look comfortable on the left. I thought he did quite well and he set up our goal," Hodgson said.
"It is looking for things to say he didn't play well in that position because I think he did."
England are back in action against Uruguay on Thursday.
