"Anyone can miss a penalty. They were not nonchalant," Hodgson said.
Euro 2012: Roy Hodgson positive despite defeat
"Ashley Young's smashed against the bar and Ashley Cole's was well saved by Gianluigi Buffon."
He told BBC Sport: "A player's reputation should not be forged on a penalty shoot-out, their reputation should be forged on the four games and in those four games we have not lost.
"We stuck to our guns right until the end and the players should be very proud of what they did.
"I have learnt a lot about the players and their determination and dedication to the task and the fact they are so keen to play for England.
"There were some heroic performances not only tonight but also in the previous three games."
England keeper Joe Hart failed to save any of Italy's penalties, with the Azzurri's only failure coming when Riccardo Montolivo sent his effort wide.
England's penalty woe
England's penalty record stands at six defeats and one win from seven shoot-outs at major tournaments.
They lost to Germany in 1990 and 1996, to Argentina in 1998, to Portugal in 2004 and 2006 and to Italy in 2012.
They beat Spain in 1996.
From 35 shoot-out penalties taken they have scored 23.
"I went in confident we would win the game," said Hart. "I was required to step up and didn't make the saves.
"They were superior in regards to chances, but we were very resolute and gave everything when defending.
"I face penalties against [Manchester City team-mate] Mario Balotelli on the training ground and I felt confident, but he took a good penalty.
"Of course I expect to make saves, I feel like no-one can beat me.
"We've lost at the end of the day, but I don't think anyone has let the country down and we have adapted well to the manager."
Hodgson had his players practising penalties in the build-up to the game and he had hoped they would be able to improve England's dire record in penalty shoot-outs.
"When we took it to penalties I was rather hoping it would be our tournament to win on penalties. Certainly the practising didn't help us too much on this occasion," he lamented.
"Maybe it's just fated at the moment that we don't win on penalties but I really can't fault any of the players for their effort.
Jurgen KlinsmannMatch of the Day analyst
"Italy were far superior to England. What impressed me was technically they controlled the game, but also they were physically stronger. That surprised me, and they deserved to get into the semis where they will expect a good clash with Germany. I had hopes for England but to be honest they didn't deserve it because they could not keep tempo with Italy, they didn't close down spaces and it was too big a mountain to climb."
"At the end we had lots of players out there running on empty, with very tired legs, fighting off cramp, but they kept us in there until the end and when you go to penalties you do have a chance, but unfortunately Italy took the chance and not us.
"Penalties has become an obsession for us in English football and in training the players have done extremely well.
"But you can't reproduce the tired legs. You can't reproduce the pressure. You can't reproduce the nervous tension.
"[The Italians] stood up to it better than we did. Pirlo's [dinked] penalty was the perfect example."
England almost took the lead when an early Glen Johnson effort was saved by Buffon but they were on the backfoot for most of the game as Italy went close with several chances as well as hitting the woodwork twice.
"I thought the chances were there for both teams but as the second half went on we tired very badly and they came at us again and again," said Hodgson.
"We have lost and we have gone out without losing a game with our heads held high."
England's next competitive game is a World Cup qualifier against Moldova on 7 September and, despite their Euro 2012 exit, Hodgson has been impressed by the qualities shown by his squad.
"I've been very happy with what I have seen from this group of players and how they have dealt with the demands of an England shirt," he said.
"I do think we have got some very good young players coming through and this tournament has been very good for them."
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