Despite the disappointment, it marked further progression for the Three Lions who reached the semi-final stages of the World Cup in 2018 in what was Southgate’s first campaign in charge of the Three Lions.
Southgate is under contract until after the 2022 winter World Cup in Qatar with the FA keen to extend his deal.
And while the 50-year-old says he wants to remain in charge for that competition, he was non-committal on a new deal.
‘I don’t think now is an appropriate time to be thinking about it,’ Southgate told a press conference on Monday.
‘We have to qualify for Qatar. I need time to go away and reflect on Euro 2020. I need a rest.
‘To lead your country in these tournaments takes its toll. I don’t want to commit to anything longer than I should. It’s not a financial thing. As I sit here today. I would be wanting to take the team to Qatar.’