Southgate handed Phillips his England debut in September 2020 and the Whites midfielder has now amassed 23 caps for the Three Lions, becoming an integral member of Southgate's midfield.
The England boss came under fire from fans as this month's winless run of four Nations League games ended with a 4-0 defeat at home to Hungary but FA chair Debbie Hewitt has issued strong backing for Southgate ahead of this winter's World Cup in Qatar.
Phillips started every game of last year's European Championships in which Southgate's side were beaten by Italy on penalties in the final.
Three years earlier, the Three Lions reached the semi-finals of the 2018 World Cup.
"Based on any facts on the pitch, he is the most successful England manager we've had for 55 years," said Hewitt, as quoted by BBC Sport.
"But the bit people don't see is the culture he's created.
"Prior to Gareth being the manager there was not the pride of wearing the England shirt. There was a club rivalry we would read about, players not getting on.
"He's changed that beyond recognition and I've seen that for myself.
"I've worked in business and Gareth's skills, his high IQ, would make him a chief executive in any sphere.
"That resilience and accountability. There's no sloped shoulders, and that's what you want in an England manager."
The FA handed Southgate a contract extension to 2024 in November of last year, opting to do so before this year's World Cup, after which his previously existing contract expired.
The England boss has been reassured by the FA after a haul of just two points from four Nations League games left the Three Lions bottom of their group.
Hewitt added: "The fact there's been a stumble does not make us automatically say 'should we have given him a contract?'
"We have confidence in Gareth for all the reasons I described and I think that's the important thing. And it's particularly important going into the biggest tournament.
"Gareth's reaction (to her call), as in everything with that sort of conversation, was that it is his accountability, that 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."