The Blues put in a solid performance at Wembley to beat their title rivals 2-1 on Sunday.
Marcos Alonso netted a brace as Chelsea bounced back from their opening day defeat to Burnley.
Conte has endured a challenging summer following their title glory in May.
Chelsea have failed to land many of his top targets and the Italian is now under pressure to deliver.
Player-turned-pundit Neville, though, believes thanking his team was unnecessary after the Spurs win.
“It was interesting the quotes from Antonio Conte at the end of the match, thanking his players,” Neville said on Sky Sports.
“I wouldn’t say he would have been shocked or surprised by what he saw yesterday, but I think with the negativity, I mentioned before the game it could unravel at Chelsea pretty quickly and he wouldn’t have known what to expect.
“His players dug in, they were resilient, they stuck to the game-plan, they were everything he would have wanted to be playing against a team in far better form, far better enthusiasm and positivity, and I think Chelsea stood up to it.
“They were really well tough in the game, I think every single one of them deserves credit.
“We’ve seen that Chelsea group over many years turn very quickly and it can get very nasty and moody.
“I thought yesterday this was a big game for Antonio Conte, and it meant more than three points.
“He thanked his players at the end, he shouldn’t have to thank his players, but he did and I think that was just a relief to how the game had gone.”
Jose Mourinho experienced players turning on him when sacked in the 2015/16 campaign.
And Conte will hope Chelsea don’t go down a similar path this term.
His side are next in action on Sunday when Everton travel to Stamford Bridge.
