The cross-code star was sent off with just 25 minutes on the clock during Saturday's match, after catching Lions wing Anthony Watson flush on the head with a shoulder charge.
All Blacks coach Steve Hansen confirmed Williams would plead guilty to a charge of unnecessary contact with the head when he faced a hearing at the New Zealand Rugby offices in Wellington on Sunday.
That hearing resulted in a four-week suspension being imposed on the centre, whose place in the All Blacks' squad for next weekend's decisive third Test has been taken by Malakai Fekitoa.
"Just finished my hearing, ended up getting four weeks," said Williams.
"I'm obviously really disappointed, but happy with being able to get in there and say my piece.
"They've come to the conclusion that it was reckless, it wasn't intentional.
"I've got in contact with Anthony and I've apologised to him, but very disappointed that I was sent from the field last night and let my brothers down."
Williams is the first All Black to have been dismissed in a Test match for 50 years.