Chelsea's Eden Hazard in action with West Ham United's Michail Antonio and Mark Noble
Slaven Bilic's side were poor for long periods and once again conceded late on at the Bridge to drop points, just as they did last season.
Antonio Conte got life in West London off to a winning start thanks to a penalty from Hazard and a fine late strike from Diego Costa.
West Ham looked like they may go on to snatch an unlikely point when James Collins smashed home a superb half volley in the box to make it 1-1 in the second half.
Some lackadaisical play in possession on the halfway line gifted Chelsea a counter attack and Costa punished the Hammers with a fine finish into the bottom corner from outside the box.
Under the spotlight: Eden Hazard
Hazard under the spotlight
Hazard, who was heavily criticised for his poor form in Chelsea's spectacular collapse last season, picked up the man of the match award after the game and was hailed as 'always world class' by Blues skipper John Terry.
But Sky Sports pundit Neville, back on TV after a failed stint as manager of Valencia, expects much more from the Belgian playmaker.
'The mentality of being a world class player means you go for it all of the time'
"We gave him man of the match, because he was the best player on the pitch," Neville said on Monday Night Football.
"But we've seen it before with him over the last two or three years that when he gets confident in a game and when he's up and he's got the game by the scruff of the neck, in the palm of his hand he's got to go for the kill and he doesn't, he steps off.
"There were 54 minutes on the clock ... and he'd gone into walking mode, standing still and walking.
Chelsea's Eden Hazard celebrates scoring against West Ham
"Showing 'I'm the boss, I'm arrogant, I've won the game'. It's 1-0, it's a Premier League match. There were three or four instances and I was not surprised when he (Conte) took him off. He'll have been seeing this.
"He's a world class player as John Terry says, but the mentality of being a world class player means you go for it all of the time and you do not change your mentality during a match."
Harsh or fair?
Neville's criticism may seem harsh but those are the standards expected of a player who is often mentioned in the same breath as the likes of Cristiano Ronaldo and Lionel Messi.
Whether Hazard takes Neville's advice on board remains to be seen. One thing is for certain, though, if Italian taskmaster Conte feels the same it won't continue for much longer.