Williams was given the red card by referee Jerome Garces for a no-armed tackle on Lions winger Anthony Watson with the score locked at 3-3 at Wellington Regional Stadium.
It made him the first All Blacks player to be sent off during a test match since Colin Meads at Murrayfield in Edinburgh in 1967, and the third overall.
New Zealand loose forward Cyril Brownlie was the first international player to be sent off against England at Twickenham in 1925.
"The impact of the red card was pretty obvious," All Blacks coach Steve Hansen told reporters.
"Sonny didn't use his arms so put himself at risk and he collected young Anthony's head and put him at risk, so we don't want that and the referee deemed it a red card so off you go boy.
"If the ref says it's a red card then you don't have a say in it. There's now a process and we'll accept that decision."
Lions coach Warren Gatland added the card had also been instrumental in the outcome of the game, with the All Blacks unable to attack through the midfield as much as they wanted while it also created holes out wide.
"It was a significant loss for the All Blacks in terms of a key man and we are aware of that," Gatland said. "There is no doubt that without Sonny Bill Williams there it created some opportunities for us."
Williams was not the only disciplinary issue on Saturday with the Lions reduced to 14 men for 10 minutes in the second half when prop Mako Vunipola was yellow carded by Garces for driving his shoulder into Beauden Barrett's head at a ruck.
Garces consulted television match official George Ayoub and despite the parochial crowd screaming for a red while they watched the replay on the big screen decided it was only worth a yellow.
Hansen refused to get drawn on the differences between the two offences, preferring instead to state he believed both were unintentional.
"I don't think Sonny intentionally went out to hurt the player," Hansen said. "Did Vunipola intend to take Barrett's head off? I don't think so. Things happen in the heat of the moment."
(Reporting by Greg Stutchbury; Editing by John O'Brien/Jeremy Gaunt)
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