Wellington Hurricanes captain Savea ran his thumb across his throat during a verbal exchange with Melbourne Rebels halfback Ryan Louwrens after being shown a yellow card in Friday's match, won 39-33 by the Hurricanes.
Savea, regarded as one of the world's premier players, was shown the card for "escalating" the situation according to referee James Doleman, with players from both teams having become involved in a fracas late in the first half.
Rebels captain Reece Hodge complained immediately to Doleman that stiffer punishment was needed as Savea's gesture towards Louwrens was "threatening to kill him".
Savea, who has played 70 Tests for the All Blacks, including four as captain, later told broadcaster Stan Sport he lost control of his temper and regretted the action.
"I can understand the fans are furious around the gesture that I made," he said.
"Kids are watching us, we're in the heat of the moment. Usually that's out of character for me, so I put my hand up first and I apologise for that."
Savea said the fiery encounter with Louwrens was "just normal banter in the game" and accepted it wasn't a good look from a player regarded as a role model.
"We're trying to clean up the game. I understand, there's no excuse for me, I've got to be better."
Savea's action overshadowed his dominant on-field performance at No.8, having scored the first two Hurricanes' tries and set up the third.
Follow all the action from the Super Rugby season on Flashscore.
