Wilshere, Shaw relieved with draw
England were already eliminated when they walked out onto the Estadio Governador Magalhaes Pinto in Belo Horizonte, while Costa Rica had a round-of-16 berth in their pockets and although the English took more shots and had more possession, they had to settle for a 0-0 draw.
With a younger, more inexperienced squad than they traditionally send to a major tournament, England had initially tried to play down their hopes in Brazil but, as the World Cup got closer this year, they were unable to reel in the expectations of themselves, the British media and their fans.
A pair of 2-1 defeats to Italy and Uruguay saw Hodgson's men eliminated, however, and their lack of belief was evident following a scoreless draw with Costa Rica - a country with less than a tenth of the United Kingdom's population and ranked 18 spots below England by FIFA.
"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," Wilshire told Radio 5Live.
"We created a few chances and we are just happy we didn't lose all three of our games."
Shaw added: "It would have been a massive downfall to go home with zero points."
The positive for England in Brazil was the experience gained by some of their up-and-coming players such as Shaw, Ross Barkley and Raheem Sterling.
Shaw became the second youngest English player to start a game at a World Cup behind former Liverpool striker Michael Owen and the 18-year-old could barely contain his excitement in Belo Horizonte.
"It was amazing to be playing in the biggest tournament in the world, a dream come true," the Southampton defender said.
"I don't want to stop here, I want to keep getting better and better."