The recently-appointed boss oversaw his side struggle to contain a superior Italian outfit, but has maintained that the national setup must be their own team in order to succeed at the highest level, and not try to emulate others.
"We have to maintain that degree of pragmatism that we have always had in English football," Hodgson told Press Association.
"We also have to retain that fighting spirit and doggedness. We mustn't start throwing those qualities overboard just so you can come off the field and have someone say you've had more shots at goal.
"I don't want to emulate nations, no. I want England to be England.
However, Hodgson is aware that England have much room for improvement following their quarter-final exit but citied the recent success of world and European champions Spain, who also suffered a similar barren spell on the international scene to the Three Lions.
"You can't say we are going to play like Spain because apart from anything, the Spanish grew up in different climatic conditions to us and have always had very different qualities,” he added.
"And let's not forget that for years and years Spain went to every major tournament and never achieved anything."
Asked if England have enough upcoming talent to provide the national side with a steady stream of good players, Hodgson was positive about the future of the squad.
He continued: "Jack Wilshere had an impact before he missed the whole of last season with injury. If he can reach that level he's got to be a player who's of interest to us. Adam Johnson is another who's quite interesting.
"Then there were talents like Alex Oxlade-Chamberlain and Danny Welbeck, who were with us at the Euros. They are not poor players technically. Hopefully in two years' time they will be even better."
Hodgson must now look on to their World Cup qualifying campaign, which gets underway in Moldova on September 7.