The returning Steven Pienaar scored early on and Argentine front man Denis Stracqualursi scored the second to ensure Andre Villas-Boas and his team left Merseyside with nothing.
Former Manchester United defender Neville told Everton’s official website: “I said if anyone in the world could come back to this club – and I got the mickey taken out of me – it would be Steven Pienaar.
“He seems to have a spiritual home here, the fans love him and the players adore him. He got us off to a great start and it was just what we needed.”
Neville has also been impressed by the performances and work ethic shown by Stracqualursi and believed he deserved his goal.
He added: “You have got to say a quiet word for Denis Stracqualursi as well for the last three home performances he has put in.
“We marvel at the likes of Steven Pienaar but Denis’ attitude really epitomises all three performances.”
The Toffees' skipper is also claiming an assist for the striker’s goal after a crunching challenge on Ashley Cole led to the score being doubled.
“I just do my job. It was a 50/50 and I won the ball. Landon played a terrific ball in and Denis scored. He got his rewards - but I'll claim the assist,” he said.
"We aren't getting carried away but our supporters will enjoy that. They've not enjoyed too many home games this season and it's up to us to continue the momentum."