Costa Rica had already secured progress to the knockout stages thanks to shock wins over Uruguay and Italy - while England knew progress was impossible having fallen to 2-1 defeats to both aforementioned sides.
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"We showed today what a good team we can be," he told ITV.
"I'm so disappointed not to finish with a victory but I don't think I could have asked for a much better performance.
"Apart from the first 10 or 12 minutes of the game I thought we dominated it totally, but unfortunately we didn't take our goal chances.
"Had we taken them, it would have been a comfortable victory."
Daniel Sturridge was the chief culprit when it came to chances spurned as the majority of England's openings fell to the Liverpool striker.
Only a wasteful shot wide following a slick 65th-minute one-two with Wilshere stood as a particularly glaring miss, however, and Hodgson declared himself satisfied with England's creative play.
"We created the chances, that’s important, and normally Daniel is so clinical," he said. "I'm not that concerned, I know he will take the golden chances in the future.
"The important thing is to keep giving him the opportunities.
"I've got to say that today we were really unlucky not to win this game and I'm pleased that, at least, we've given the fans something to cheer about in terms of our performance."
Defensive shortcomings undermined England in the decisive 2-1 losses to Italy and Uruguay and Hodgson was pleased to see a new-look backline featuring Phil Jones, Chris Smalling and Luke Shaw help recalled goalkeeper Ben Foster to a clean sheet.
"I thought they all did very well," he added. "I thought the whole back four was absolutely excellent.
"We restricted the team that's beaten Italy and Uruguay and topped the group to almost no chances and Foster was very good behind.
"In midfield we outplayed them in that area, created more chances but we didn't unfortunately manage to take them and that’s a great disappointment."