Southgate undeniably had England playing on the back for after the early goal. He should have put the boot on the throat of the opposition while they we were still stunned but because he didn't victory was not only not his, it would not have been deserved had he won the pk shootout.
But having to go is a different matter altogether. He can claim success that exceeded all expectations, even if it's true no trophy was brought "home". I'd stick with Southgate, if for no other reason than there is no other realistic option. England wouldn't dare, surely, even think of Mourinho, Wenger, Howe, Allardyce, Parker or Dyche.
So to whom does England turn if the FA decide to sack a manager who brought England within touching distance of both a World Cup and Euro cups?