Williams was handed a four-match suspension after being red-carded last week for his shoulder charge against Anthony Watson.
He was the first All Black to be sent off in a test in 50 years. The last, Colin Meads, was sent off in a 1967 game for kicking another player, before red cards had been introduced.
Saturday's ill-judged tackle left the All Blacks one man down. They lost 21-24 to the British and Irish Lions, setting themselves up for a tense deciding match this Saturday.
After he was handed the ban Williams said he was "very disappointed" to have been sent from the field, adding that he had let his "brothers" down.