The England boss made nine changes and fielded the country's second youngest starting lineup at a World Cup in their final match of the tournament on Tuesday after defeats by Italy and then Uruguay had already condemned them to an early exit.
Avoiding the embarrassment of three losses came as a welcome relief to Hodgson, who felt his side deserved a first win with striker Daniel Sturridge missing a couple of good chances as England took charge of the match in the second period.
"It's hollow. We showed today what a good team we can be. I'm so disappointed not to finish with a victory but I don't think I could have asked for a better performance," he said.
"Apart from the start, I thought we dominated.
"We were really unlucky not to win this game. I'm pleased we've given the fans something to cheer about in terms of our performance."
The opening defeats that ended England's ambitions had been blamed on careless defending, with Hodgson opting to retain only Sturridge and centre back Gary Cahill for the clash against the impressive Costa Ricans.
Wilshere, 22, said the young side, which featured 18-year-old Luke Shaw making his first start at fullback, showed the future was bright despite their worst World Cup showing since 1958.
"We are professionals, we had to play for a bit of pride and show we really do love playing for the country. We showed great character to deal with the heat and not let our heads go down," the Arsenal player told BBC Radio 5 Live.
"We were nervous in the first half, it was important to get the ball down and the last 25 minutes of the first half we dominated. We created a few chances and we are just happy we didn't lose all three of our games.
"You saw through this tournament we have some good young players."
Hodgson said he had been impressed by the performance of the young players with the experienced duo of Gerrard and Wayne Rooney only coming on in the final quarter as the 1966 winners pushed for a winner.
"I think they all did very well," he said.
"I thought the whole back four did very well. We restricted the team that beat Italy and Uruguay to very few chances. We created goal chances but unfortunately didn't take them."
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