Kane's three goals helped England to a 6-1 victory over Panama which secured qualification to the Round of 16 and Neville believes the forward is one of the world's best.
He told 'ITV': "[Kane's] 2016 tournament was poor, his lead-up to this tournament was difficult between the injury, the goal that he claimed that brought a bit of pressure, but he is the most important player for England. This is a top player, a world-class player - and we don't have many.
"We're always accused of getting carried away as England, but when we do have a player that I think every team in the tournament would want, we should get carried away; we should get carried away by him.
"We're always managing expectations but this guy is the real thing, he's the real deal."
Kane's hat-trick took his tally for the tournament to five, one ahead of Cristiano Ronaldo and Romelu Lukaku to lead the Golden Boot.