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England beat Denmark 2-1 at Wembley Stadium to book their spot in the final on Sunday.
An own-goal from Simon Kjaer and a strike from Harry Kane in extra-time saw England progress on a famous night.
Southgate's charges face Roberto Mancini's Italy following a superb tournament, with ITV pundit Neville showering him and his coaching staff with glowing praise.
In doing so, he took a shot at the Prime Minister as he hailed the leadership qualities of the Three Lions boss.
Neville said: "I have to say Gareth Southgate his team, the staff the players everyone have been absolutely unbelievable and this crowd is mesmerised being in this stadium right now.
"The standard of leaders in this country over the last couple of years has been poor but looking at that man there that's everything a leader should be.
"Respectful, humble, tells the truth, genuine, He's fantastic Gareth Southgate. He really is unbelievable and has done a great job."
Roy Keane also spoke highly of Southgate, saying he's done a brilliant job and deserves all the credit in the world.
"Gareth really deserves all the credit in the world," said the Irishman.
"He's done a brilliant job, absolutely brilliant job, I'm delighted for Gareth and England deserved it.
"Man of the match was probably Kasper Schmeichel and that says a lot. Lucky with the penalty, but England deserved it."
Featured Image Credit: PA/ITV