He's come fourth place at a World Cup and runners up at a Euros. The only manager to equal or better that record is Alf Ramsey. I'd argue as have an inferior squad (in comparison to the quality at the time) to pretty much ever other squad we've taken to a major tournament since the mid 80s.
Most people don't really appreciate how good of a job someone did till after they leave. We didn't appreciate the job McLaren did at Borontill after Southgate, we didn't appreciate the job Karanka did till after Monk. We didn't appreciate the job Robson did at England till after Taylor, we didn't appreciate the job Erikson did till after McLaren. All of those managers were criticised and (in some cases) hounded out despite achieving a level of success that managers preceding them failed to achieve. We'll have the same with Southgate, he'll move on, we'll get a manager willing to go more attacking and we'll get torn apart by the teams we're beating and drawing with now. And then we'll all realise why Southgate was playing a more cautious style.
It's amazing how 4 years ago everyone went into the tournament saying we had the worst England side in living memory, and people said the same 2 tears ago. Yet after Southgate managed to take us further in the World Cup than any managers other than Ramsey and Robson, and further in the Euros than any England manager, he's the one holding us back.