Despite low expectations at the start of the tournament, the Three Lions equalled their impressive campaign at Italia '90 by reaching the semi-finals in Russia.
Although the dream of a first World Cup triumph since 1966 came to an end with a 2-1 extra-time defeat to Croatia, former England defender Neville was eager to praise Southgate's charges for making the country dream of glory.
"The first thing to say is this team has taken us to a place we never imagined we could get," Neville told BBC Sport.
"I said before the tournament England never overachieve. This team has overachieved getting to the semi-final and they can all be absolutely proud. They have taken the nation with them. You see all the fans out in the park to see them. I never thought I'd see scenes like that this World Cup. They can be absolutely proud.
"We did say before the game these lads have to take this opportunity because it may never come again and all I hope as I look at them now crying, disappointed, upset, is that they get another opportunity as good as the one they've just had."
England still have a chance to secure their best World Cup finish since 1966 when they face Belgium in Saturday's third-place playoff in St Petersburg.