Williams slapped with four-week ban
Williams was sent from the field 25 minutes into the Test after a cheap-shot, shoulder charge to the head of Lions wing Anthony Watson.
The punishment rules Williams out of the deciding Test next weekend after the Lions levelled the series with a 24-21 victory in Wellington.
Williams, who did not contest the charge, appeared before an all-Australian judicial panel in a near three-hour hearing on Sunday at the New Zealand Rugby offices.
"Just finished my hearing, ended up getting four weeks. Obviously really disappointed, but happy with being able to get in there and say my piece," Williams said after nearly three hours in front of a judicial disciplinary panel.
"They've come to the conclusion that it was reckless, that it wasn't intentional. I've got in contact with Anthony and I've apologised to him but I'm very disappointed that I was sent from the field last night and that I let my brothers down."
All Blacks coach Steve Hansen confirmed before the hearing that Williams would plead guilty.
"There's a [judicial] process, we trust the process. Sonny's paid a big price. The team's paid a big price for him making a mistake," Hansen said.
"He's disappointed. Not for himself, he accepts he's made a mistake, but he's disappointed because he's let the team down."
The All Blacks have already called Highlanders centre Malakai Fekitoa into the squad as Williams' replacement with senior midfielder Ryan Crotty already sidelined by a hamstring injury sustained in the first Test.
Although the All Blacks were forced to play with 14 men for 55 minutes after Williams was sent from the field, the Lions did not hit the lead until three minutes from fulltime when Owen Farrell landed the match-winning penalty for a 24-21 victory.
The All Blacks won the first Test 30-15.
Williams is the third All Black to be sent off following Cyril Brownlie in 1925 and Colin Meads in 1967.