Roy Hodgson is unsure whether managing England will prove the final chapter of his long and varied career in football.

Iceland, the smallest nation to ever grace a major tournament, inflicted one of the most humiliating defeats in English football history on Monday, deservedly securing a 2-1 victory in their Euro 2016 last-16 clash on the French Riviera.

The squad jetted back from Nice the following day, returned to Chantilly to pack their bags and flew back across the Channel nursing wounds that will take a while to heal.

Outgoing England manager Hodgson had planned to go with them, only to be reluctantly persuaded to speak to the media alongside Football Association chief executive Martin Glenn.

Clearly emotionally drained, the normally expressive 68-year-old was unable to look far beyond his current predicament when asked whether he would be staying in football after 40 years in coaching.

"I don't know yet," he said. "It's a bad day to ask me. At the moment football isn't my favourite subject."

England's Euro 2016 struggles are unlikely to put clubs off the well-travelled coach, with iRENA, the main sports agency behind the boom in the Chinese Super League, saying he is sought-after in China.

It would be a voyage into the unknown for Hodgson, who was visibly shaken and fragile following Monday's humiliation.

His focus may be elsewhere, but the FA has quickly turned its attention to finding a successor, with England Under-21s manager Gareth Southgate the overriding early favourite with the bookmakers.

Chief executive Glenn said nationality would not be a factor in the new appointment, but Hodgson would be proud to see an Englishman succeed him so long as they were the best candidate.

"I don't have a problem with it," he said when asked about the spectre of a foreign successor. "It would be very hypocritical of me to do so having been a national coach in Switzerland, Finland the UAE.

"I think I should be the last person to say it's got to be a national. It's got to be the best person.

"I think it would be nice if it was an Englishman. I have been proud as an Englishman to do the job and I have had a lot of support from the general public as an Englishman. But Martin will have to find the best person available."

Hodgson's discomfort at facing the media less than 24 hours after resigning was clear, making it hard for him to reflect on what went so wrong in France.

The finality of his dressing room announcement meant no players tried to get him to reconsider his decision to quit, with the 68-year-old leaving saddened and confused by England's sorry exit.

Hodgson downplayed the issue of tiredness, but admitted the level of performance against Iceland "shocked us a bit", leaving England's squad bruised but with the potential to achieve in the future.

"I have tried over four years to do the best job I could do," Hodgson added.

"The results will show it wasn't good enough because the best job you can do is win a tournament. We haven't come close to it. As a result I expect that myself and the team will be criticised.

"But I certainly don't feel that I need to be Uriah Heep-ish about it in any way. I think personally the team has got better. I personally think we have made progress.

"I personally think the team in 2016 is better than the team which reached the quarter-final in 2012, but that's my personal opinion and I am entitled to it and I have to accept if you say it's not true and the team is as bad today as it was then."