Rooney was deployed on the left during the first half and struggled defensively before supplying the cross from which Daniel Sturridge scored the equaliser.
In the second half, Rooney was moved out to the right-hand side, with the Manchester United striker positioned out wide to accommodate Liverpool teenager Raheem Sterling.
His performance against Italy led to suggestions that Rooney could be dropped for Thursday’s Group D game with Uruguay, but Hodgson sprang to the defence of the 28-year-old.
"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," said Hodgson.
"It is looking for things to say he didn't play well in that position because I think he did."
Hodgson felt his side were unlucky to lose to Mario Balotelli's winner after Sturridge had cancelled out Claudio Marchisio's opener.
He added: "It is a bit tough to accept we lost the game. Joe Hart has had a pretty quiet evening but we found ourselves having lost it.
"Even when they got back to 2-1 I thought we would get back into it. I thought that was the best I'd seen the team play.
"I suppose you have to bite the bullet today and accept we played well.
"I thought we came to terms with it much better in the second half. We are a positive team who do not sit back and we left one or two opportunities for them, but we had chances to score.
"Our final ball was disappointing and we are better than that, but we are a young team and this is a first World Cup for two thirds of the team and it is something we will improve upon going forward.
"It isn't a perfect start, but we don't live in a perfect world.
"To take them so close gives us great confidence playing against Uruguay and Costa Rica."
He added: "The fact is that if you lose the first game you probably have to win the next two.
"The teams you play against have to win as well, but there is no way you can drift into the second round.
"Italy have the best start, as have Costa Rica, and we and Uruguay are on the back foot.
"We now play Uruguay and Costa Rica, so at least our fate is in our hands."
Sturridge hobbled off in the second half, but Hodgson confirmed the striker only suffered a dead leg.
England's only injury was to physio Gary Lewin, who broke and dislocated his ankle after landing on a water bottle during the celebrations for the equaliser.
Italy, meanwhile, are now overwhelming favourites to qualify.
Coach Cesare Prandelli was happy with his team's display, but lashed out at officials for not allowing drinks breaks in the 30 degree heat.
He said: "It's truly absurd we cannot consider a time-out.
"If we want entertainment, we need to enable the players to give great performances."
Prandelli, who knocked England out of Euro 2012 with Italy, lavished praise on Hodgson's team.
"Physically, we were a bit better than England, but I think England are one of the strongest teams at the World Cup," he said.