The 51-year-old coach has recently come under fire from fans and pundits - but the Football Association has backed Southgate and told him that his position is safe.
England are in danger of being relegated from the Nations League's top tier, following their 4-0 defeat at home against Hungary.
However, Debbie Hewitt - who took over as FA chair in January - has urged fans not to overlook Southgate's past successes, including taking England to a World Cup semi-final and the final of Euro 2020.
Hewitt told journalists: "My personal opinion on Gareth is that he is, by the facts on the pitch, the most successful England manager we've had for 55 years.
"The bit people don't see as much is the Gareth at camp and the culture he's created.
"Certainly prior to Gareth being the manager of England, there was not the pride of wearing the England shirt. There were the club rivalries we'd read about. The players not getting on.
"He's changed that beyond recognition and I've seen that first hand."
Hewitt also revealed that Southgate has been typically measured in his response to recent results.
She said: "Gareth's reaction, as in everything to that kind of conversation, is always 'it's my accountability, and there's always something to learn'.
"That's why it's refreshing working with somebody like that because that openness to learn is quite remarkable and quite unusual in any sphere."
Southgate's current contract expires in 2024, and he's poised to lead England at the World Cup later this year.