Roy Hodgson has insisted his enthusiasm to lead England has not been dimmed by his team’s toils in Brazil and the manager is convinced this group of players will be “better and stronger” as they move forward towards the 2016 European Championship.

England’s elimination from the World Cup was confirmed on Friday – when Costa Rica beat Italy 1-0 – with this their briefest appearance at the tournament, amounting to three group games and 10 days, in 60 years. Hodgson is considering giving the likes of Ross Barkley, Luke Shaw and Jack Wilshere starts in Tuesday’s final match against the group leaders, Costa Rica, when Steven Gerrard and Frank Lampard are expected to bring the curtain down on their international careers.

It is unclear whether either of the veterans will play at the Estádio Mineirão, with England to depart for London, via Rio de Janeiro, immediately after the game in Belo Horizonte. Regardless, Hodgson, who has received the public backing of the Football Association to complete his four-year contract, is already planning for the Euro 2016 qualification campaign. “My enthusiasm for football will not wane, and my enthusiasm for working with these players is not likely to wane either,” the manager said. “I believe that England have got a very strong basis for a team.

“I think this team is still very young. These players, in the space of two more years playing in the Premier League, as they will have, have got to get better and stronger, but playing together as an England team will make them better and stronger. I’ve never doubted for one minute that as this team moves forward, not just to 2016, but even on from there, they will become stronger and better. We will just, for the moment, have to suck on this very, very bitter pill that their hopes and dreams have floundered here because we weren’t able to win the first two group games. But the experience bodes well for the future.”

If, as expected, Gerrard confirms his retirement after a 14-year career at this level – he earned his 113th cap against Uruguay and is just two shy of David Beckham’s record for an outfield player – then Hodgson will have to identify a new captain to lead the team to France in two years’ time. Joe Hart and Wayne Rooney would be strong candidates, the latter having captained the side twice over his 94-cap career, and Hodgson envisages the Manchester United forward remaining a mainstay of his side.

“We haven’t got many older players,” Hodgson said. “Wayne Rooney is 28 years of age, coming on 29. I’ve got to be honest with you, I don’t regard 29 as old. Most of those players playing for Uruguay on Thursday were 29 plus. And Steve Gerrard and Frank Lampard are the only two real 30-year-olds we have.

“I don’t have any regrets. I don’t think the team let anybody down against Uruguay. I think everybody worked very, very hard. I don’t think that we could have put out a team that could have done any better against Uruguay. We were undone by the two goals by Luis Suárez. So, no, I don’t have any regrets. But results colour everything.

“It’s very hard to be happy when you’ve lost. Results colour your judgment, colours everybody’s judgment. I’m certainly happy with the way the players have prepared for these games and the way they have approached the tournament. I’m really happy with the dedication and effort they have put in. But we’ve played two experienced and strong teams in Italy and Uruguay and, on both occasions, we’ve come out second best.”