England’s worst home loss since 1928 leaves the Three Lions facing the ignominy of relegation from the top tier of the Nations League.
But it is the impact such an embarrassment will have on Southgate’s preparations for the World Cup in five months’ time that is the most pressing concern.
England have only two more matches, away to Italy and home to Germany in September, before starting their World Cup campaign against Iran on November 21.
The switch to a winter World Cup due to the climate in Qatar created a quirk in the calendar that forced international sides to play four matches this month after a physically exhausting campaign for many players at club level.
World champions France are also bottom of their Nations League group without a win in four games, while Belgium’s Kevin De Bruyne and Dutch manager Louis van Gaal have criticised the punishing schedule.
Southgate pointed to that as a major factor in England’s failure to win in four consecutive games for the first time in his six-year tenure.
“This has been a really unique set of fixtures,” he said. “I was concerned about it before because I knew we were going to have to make changes and we couldn’t field a full team for every game.
“I tried to give some young players experiences and rest some of the players I think have had long seasons. We are going to need them in the World Cup and we didn’t want to break them.”
– ‘Sacked in the morning’ –
Captain Harry Kane and Raheem Sterling were quick to shut down any questions over Southgate’s future given the credit he has in the bank for not only reaching the final of Euro 2020 but also the semi-finals of the 2018 World Cup.
However, it was the manager who was the target for abuse from a frustrated crowd as Hungary ran riot in Wolverhampton.
The 51-year-old was derided with chants of “sacked in the morning” and “you don’t know what you’re doing.”
Southgate admitted earlier this week that he will not “outstay his welcome” as national team boss as criticism of his conservative approach persists.
Critics of the former Middlesbrough boss, who favours two defensive midfielders in his line-up, believe he has been too slow to embrace the array of attacking talent at his disposal.
Manchester City pair Phil Foden and Jack Grealish are just two of the creative options whose chances to shine on the international stage have been limited under Southgate.
However, he appeared to double down on his idea of how England can be successful in Qatar after such a disastrous Nations League campaign so far, which has featured just a single goal, from the penalty spot.
“I’m very clear, I know what works for us and I have evidence now of what doesn’t,” he said.
“Tonight is another example of why that core of the team has been so important and why the balance of the team has to be right.”
Southgate’s loyalty to Everton goalkeeper Jordan Pickford and Manchester United captain Harry Maguire has been questioned in the past.
But their places in the starting line-up for the World Cup look even more assured as they were rested for the Hungary mauling.
Southgate will also be hoping for a return to form and fitness for Ben Chilwell and Luke Shaw in the coming months after not naming a natural left-back in his squad this month.
There are also concerns at the other end of the field, with Southgate admitting he is worried by an over-reliance on Kane and Sterling for goals.
But he is certain he is the man to lead England to Qatar and deserves the chance to prove himself again when it matters most, at a major tournament.
“I know there will be a lot of criticism and call for change,” said Southgate. “But I go back to the fact when we’ve had our strongest teams we’ve had excellent results.”