Gregor Townsend's side ended a three-match losing streak against Australia in Sydney as it sealed a 24-19 win, Hamish Watson's second-half try proving decisive.
Defeat was a shock for the Wallabies given Scotland was without some of its star players like Stuart Hogg, Greig Laidlaw and Tommy Seymour due to British and Irish Lions responsibilities.
And one fan took to Facebook to express his anger at the loss, Jack Quigley calling the performance "a disgrace" and questioning how much the current Wallabies side care about playing for their country.
Quigley even offered to travel to Brisbane to speak to the squad and explain his anger, but Cheika opted to talk to him directly to insist his side were hurting just as much as the fans.
"I spoke to the gentleman and gave him a ring because I think it's important that we talk to the fans," he said.
"When we come out to pressers and say that we want to make the fans proud - that's not lip service - we do.
"We're not perfect at it sometimes but I think that he's expressed how he is feeling after the game and I don't think it would be too far away from - maybe not in the detail - but not too far away from how some of us were feeling about it as well.
"I spoke to him about some of the things that we are feeling, what we are trying to do around it and what some of those things are in the background.
"We're feeling the same thing as fans."
The coach also confirmed Quigley's post had been pinned on the wall of the team room, catching some of the players by surprise.
"We put the post up on the wall and that was pretty confronting for a few of the guys because they hadn't seen it - it was pretty heavy in some ways," he added.
"That's the message there and then."