England had attacked from the off, through Raheem Sterling, Danny Welbeck and goalscorer Daniel Sturridge, but Italy exposed England's defensive weaknesses to inflict defeat courtesy of goals from Claudio Marchisio and Mario Balotelli.
Hodgson knows England may have to win their remaining games against Uruguay and Costa Rica, but is confident that the team will do it.
"We had a very young and inexperienced team on the field at the end, but they made some bold moves and didn't let anyone down," he said. "That gives me great hope and confidence. If we can continue at that level, I think we can win both matches and stay in the tournament. We will prepare for them and will try to do our best to get the win we had a good chance of getting against Italy."
As Uruguay lost their opening game against Costa Rica, they too need a win on Thursday in Sao Paulo.
"It is likely to be a similar encounter to the Italy game. I think it will be cut and thrust," Hodgson said. "There will be two teams who have lost the opening game and know they have to win the next one."
Uruguay looked vulnerable to pace in their 3-1 defeat by Costa Rica on Saturday. Costa Rica, outsiders to qualify from the group, pulled apart the Uruguayan defence, and Benfica defender Maximiliano Pereira was sent off, meaning he will miss Thursday's game. However, Uruguay striker Luis Suarez is closing in on a return to full fitness from a knee injury after sitting on the bench throughout the Costa Rica loss.
"It would have been very difficult for him to come on," Uruguay coach Oscar Tabarez said after the defeat. "We still have four days before we face England. If he improves there is a chance he may play."
Sturridge and Steven Gerrard looked to be struggling at the end of the match, but Hodgson reported no fresh fitness concerns.
Foremost among the positives in the match against the four-time champions was England's attacking threat, which Sturridge hopes they can replicate.
"It's important we continue playing the way we did against Italy," the in-form Liverpool striker said. "I thought we played very well, it was just unfortunate. There were two very good sides out there, but they got the breaks and we didn't.
"We worked very hard as a team and created a lot of chances. We worked their 'keeper - if you get shots on target and their 'keeper makes good saves you have to say 'fair play'."
England landed back at their Urca base in Rio yesterday morning, where they will train today and tomorrow before flying to Sao Paulo on Wednesday. Alex Oxlade-Chamberlain stepped up his rehabilitation from a knee injury over the weekend and could be in the frame to face Uruguay.