An own goal and a Harry Kane winner saw England through to face Italy in Sunday's final.
And after the win, Neville said on ITV's coverage: "The standard of leaders in this country for the last couple of years has been poor. Looking at that man there it's everything a leader should be. Respectful, humble, tells the truth, genuine.
"He's fantastic Gareth Southgate he really did a great job."
And fans across England took to social media to praise the job the former Crawley schoolboy has done.
Paul Taylor-Burr said: "I'm 53 I've waited all my life for this feeling in actual tears THANK YOU GARETH, THANK YOU ENGLAND."
Karen Dunn tweeted: "The boy from Crawley has done us proud! (And the players weren't bad, either) #ENGDEN."
Glenda Ford posted on our Facebook page: "Our home boy Southgate's from Crawley proud to live in Crawley and very proud to be english our boys our heroes it's coming home"
@Sara_mac said: "I think it’s sad that @GarethSouthgate has been defined by ‘that penalty’ and now I’m so glad he’s defining his own history by taking England to the finals- amazing #englandvdenmark #DENENG #ItsComingHome #thankyouGareth."
@MrsEvs3 tweeted: "@GarethSouthgate you can be so so proud what a performance, what a leader - whole team has done you proud especially @sterling7 @HarryKaneMBE what a night for the country well done everyone, thank you xxx"