Young hit the bar and Cole's kick was saved by Gianluigi Buffon as Hodgson's team lost 4-2 in the shootout to an Italy team that totally dominated a game which ended goalless after extra-time.
"I don't think I could've asked for any more," said boss Hodgson. "They gave their all and we weren't quite good enough to win it over 120 minutes.
"When it went to penalties we went down the same road we've been down so many times before.
"They weren't nonchalant. Ashley Young's smashed his against the bar and Ashley Cole's was well saved by Gianluigi Buffon. A player's reputation should not be forged on a penalty shootout, it should be forged on the four games we have not lost.
"We've watched these players taking penalties in training because it has become an obsession for us in English football, and they'd done extremely well. But you can't reproduce the tension, the occasion, the tired legs."