The Leicester centre was given a free run to the line for a try after intercepting a pass from Kieran Read during England's famous 38-21 victory over New Zealand at Twickenham.
But he slowed down as the tryline approached, which Jones says showed lack of respect for the Kiwis and the game.
"England are still very young," Jones told The Daily Star. "If they can keep it together and go on and pick up 600-odd caps then they could potentially have a very good team.
"But there were already signs of arrogance at the weekend with their centre walking over the line.
"That's disrespectful to the world champions - and if they don't control that kind of thing they will not go forward as a team.
"You don't want to see that sort of thing creep into the game because it's not good for rugby.
"It doesn't wind up other teams but the game of rugby is about respect - and that's one thing we simply must keep in the game.
"New Zealand have scored numerous points against numerous teams and you never see any of their players do that. They run hard and try to get under the posts to make the kick as easy as possible.
"So why didn't the England boy do that? That's what the game is about. It's very important to keep a tight lid on that kind of attitude.
"The only guy I really know in the England management is Andy Farrell and I know he certainly will not tolerate that sort of thing. He'll be disappointed by what Tuilagi did."
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