Captain Steven Gerrard admitted England had not played the best football at Euro 2012 and needed to work harder at retaining the ball following the quarter-final penalty shoot-out defeat to Italy.
The Azzurri dominated possession and hit the post twice, and although England were able to keep them at bay for 120 minutes, the failure of Ashley Young and Ashley Cole to convert their shoot-out kicks led to an another last-eight exit for England.
Gerrard said: "At times the football hasn't been fantastic, we haven't blown people away. The possession stats speak for themselves. Moving forward as a nation we do need to improve with the ball."
Despite the less-than-impressive performance, Gerrard was happy he and his colleagues had not come up short for effort.
"Everyone has given everything they've got and that's all you can ask for," he added. "I think the supporters will agree with me that we have played for the shirt."
But Gerrard stressed: "I think we've performed to a better level at this competition than in previous tournaments."
Gerrard is keen to continue as captain and also said he was happy with his own individual performance in the tournament.
He added : "I think performance-wise I'm reasonably satisfied. I'm just in a zone of frustration and disappointment because we've come so close to ending that quarter-final hoodoo."
Gerrard was given the captaincy by Hodgson and the Liverpool midfielder revelled in the role, and he said: "I've loved it, I've loved the responsibility and I've enjoyed every minute of it."
Hodgson has also been happy with Gerrard's captaincy. Gerrard said: "I've had a brief chat with the manager, I'm available as long as I'm wanted at this level. The manager has told me he wants me to continue and carry on."