Earlier in the week, Williams caught up with All Blacks coach Steve Hansen to 'talk tactics'.
Meanwhile, Cheika said he was "bitterly disappointed" at the performance of referee Romain Poite in the Wallabies' loss, saying the match official ignored Australia captain Stephen Moore, an act he described as "blatant" and the continuation of a theme.
Cheika could be seen using what appeared to be foul language in the coaches' box following a late decision by Poite at Westpac Stadium tonight, and he didn't hold back when asked about the referee afterwards.
"Well, I was bitterly disappointed, to be honest," Cheika said. "I'm on record with the referees' boss Alain Rolland about the treatment to our captain and our players, by Romain Poite, and also by Nigel Owens over this last year.
"I'm not quite sure why, but there was a time in the game [tonight] in a break in play when the national captain of Australia [Moore] was asking the referee, 'when might there be an opportunity for me to talk to you?' And he absolutely ignored him. He's got the whistle, I understand, but there's a place where the captain has an opportunity to speak to the referee.
"The referee may not like the captain personally, that might be his prerogative, but he has to afford him that opportunity if he is affording it to his opponents. I think that attitude followed right through. David Pocock was being called off by the [assistant] referee for an HIA [head injury assessment] and the referee wouldn't stop the game. The players almost went straight through the doctor, even though he was requested by the players to stop so the player could go off.
"I don't know if it's subconscious or not, but it's there and it's got to be dealt with because it can't be that the opponents can say everything to the referee. No one is saying anything bad to him but if they've got pre-determined attitudes towards our players... I asked Alain Rolland last week when I saw him in Sydney and he said, 'no, that's a surprise to me'. But it's pretty blatant to anyone listening to the 'refs' ears'."
Asked about the treatment given him by Poite, hooker Moore, who had blood running down his face from an accidental kick during the hard-fought test, said: "I think Cheik has pretty much said it all. I think It's probably better if I leave what Cheik has said there."