For the sixth time in seven attempts since the 1990 FIFA World Cup™, England bowed out of a major tournament on penalties as Ashley Young and Ashley Cole missed from 12 yards to hand Italy a 4-2 shoot-out win.
The Azzurri advance to a semi-final meeting with Germany on Thursday, while England depart the tournament wondering what they have to do to bring an end to their penalties hoodoo.
Hodgson said he had been confident in England's five penalty-takers before the shoot-out had got underway at the Olympic Stadium. "We've watched these players taking penalties in training because penalty-taking has become a bit of an obsession for us in English football, and they've done extremely well," Hodgson said.
"But you can't reproduce the tension, you can't reproduce the occasion, you can't reproduce the nervousness."
Hodgson spoke admiringly of the composure shown by Italy's man-of-the-match Andrea Pirlo, who chipped his third penalty delicately straight down the middle as England goalkeeper Joe Hart dived to his right.
"The sort of cool calculating way that Pirlo had the confidence to chip the goalkeeper - that's something you either have or you don't," Hodgson said. "There's no amount of coaching or training that can reproduce that."
Hodgson also defended the penalty-taking records of Cole and Young, noting they had both had experience of taking spot-kicks for their clubs. "You saw Ashley Cole's penalty in the Champions League final and you've seen Ashley Young convert many penalties for Watford and Manchester United," he said. "We were confident we had five really good penalty-takers, but unfortunately for us two missed."
But England striker Wayne Rooney, who had successfully converted his side's second kick to put them 2-1 ahead, was left frustrated after yet another loss. "It's obviously a hard way to go out and it's happened too many times now," Rooney said. "Hopefully there's going to come a time when we win one."
"I did think Italy played well, I wouldn't begrudge them their victory. I thought for long periods it was an interesting tactical battle and a relatively even game because they still didn't manage to get behind our defence," he said. "Unfortunately when we did have one or two opportunities we didn't do as well with the ball as perhaps we should have done."