Hodgson's side went into their Group D campaign with low expectations and were rated even less when they trailed Sweden 2-1 following a 1-1 opening draw with France. But the introduction of Theo Walcott by Hodgson sparked England into life and they ran out 3-2 winners, meaning a draw against Ukraine on Tuesday would put them in the quarter-finals.
Football Association vice-chairman Sir Dave Richards told the BBC: "The way they all want to work for one another and the comradeship behind the scenes is quite unbelievable. It's down to Roy. He seems to have that little bit of a Midas touch/"
England had led through Andy Carroll's goal against Sweden but a Glen Johnson own goal and Olof Mellberg header put England on course for an early return home.
But Hodgson put on Walcott who scored the equaliser before setting up Danny Welbeck's winner.
Premier League chairman Richards added on Hodgson: "He's brought something a little bit different, he's very progressive in his way.
"It's something that is a little bit unique - I've never seen anything like it before.
"Everybody seems to be in a great frame of mind. The mood is fantastic and the manager is in great form."