England were optimistic that they could exceed expectations in Brazil, but that proved to be unfounded as defeats against Italy and Uruguay in their first two Group D matches ensured they will make an early exit from the tournament.
Not since 1958 have England failed to progress to the knockout stage at a World Cup, but the Football Association have backed Hodgson to stay on as manager.
Another defeat against Costa Rica at Estadio Mineirao will no doubt lead to more speculation as to whether Hodgson is the right man to take his country forward.
Costa Rica have succeeded where England have failed by beating Uruguay and Italy to surprisingly seal their place in the last 16 with a game to spare. And assistant coach Paulo Wanchope is determined to claim the scalp of the 1966 world champions in Belo Horizonte.
He said: "The players want to impress the world by getting three points against a team like England.
"I know for sure the players want to do well and end up in the Premier League. Even though we are through and they are out, beating England would still mean a lot to our team.
"We know that we can go far at this World Cup. We have just beaten another world champion and we need to enjoy that and then, against England, we will definitely play to win because of all that it would mean."
While the inquest into England's failure in Brazil goes on, Costa Rica can look forward to playing a World Cup knockout game for the first time since 1990.
Jorge Luis Pinto could opt to make changes for the final group game with qualification already secured, while Hodgson has vowed to make alterations to his side in order to give squad members who have not featured in the first two matches an opportunity.
Frank Lampard is set to captain the side, with Steven Gerrard dropping to the bench, and youngsters Luke Shaw - in for the injured Leighton Baines - and Ross Barkley are to get a chance from the start, but Alex Oxlade-Chamberlain (knee) will play no part.
Hodgson said: "I'm going to be picking the team for Costa Rica with a view that all the players who are with us get some minutes on the field, I will be changing the team to give others a chance to show what they can do.
"It's not purely planning for the future and not purely sentiment. It's to give players a chance to go home from this World Cup too early, bitterly disappointed but to be able to say they weren't here to make up the numbers, they actually took part."
If England suffer another defeat on Tuesday it will be the first time they have failed to pick up a point in a World Cup.
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