England's remarkable set-play success is the fruit of extra preparation on the training ground with attacking coach Allan Russell, who has travelled with Southgate to the United States to study strategies from the National Basketball Association and NFL.
"The pressure of a World Cup, can they handle it?", Neville told ITV.
"At the beginning we were working together with the lads and trying to sell them the vision of what's possible, what we're looking to achieve in the long term".
Councillor Judith Blake, Leader of Leeds City Council, said: "England's performances under the astute management and leadership of Gareth Southgate in this World Cup have been absolutely sensational and instilled enormous excitement and pride in people of all ages across the country and of course here in Leeds.
Over the past several days, we've enjoyed it even more because we know what's been going on back at home".
I wouldn't question the mentality of the players in the last ten or 15 years, I have played with a lot of them. Anyway, we won and the staff made this big thing about my lucky socks, saying I had to wear them next game.
"I don't know what to say in response", he said at a news conference.
On its website, the blood cancer research charity asked fans to "show your support for Gareth Southgate and the boys ahead of Wednesday's semi-final showdown - and help give blood cancer the boot".
Southgate is more interested in kicking on than wondering if they would get the kind of rapturous reception that greeted Sir Bobby Robson's men 28 years ago, although that summer left a lasting impact on him.
"It's quite unusual for me to witness all the hype and the crowds and how excited they are because that's what it must have been (like) in Italia 90 when we got to the semis", he explained.
There's zero chance of Southgate losing his job as England boss as he hurtles towards a knighthood and superstardom.
Gareth Southgate's side's potency from set-pieces was certainly on the minds of Croatia after they were forced into penalties by Russian Federation.
"You are always conscious of that because none of us are where we are just because of ourselves. So, they should - we've got trust in them doing that".
The situation is a far cry away from the bitter disappointments of Euro 2016 and crashing out at the hands of Iceland, and England as a country appear to have been united by football fever.