The governing body issued a statement on Monday saying the South African had not made the "appropriate decision".
Cheika, whose side won Sunday's match 35-34, said: "No other referee has had this stuff put out there like that.
"I would have liked my mates to back me up a little more."
Former top referee Jonathan Kaplan, who has mentored Joubert during his career, questioned whether World Rugby should be "criticising one if its own assets".
Scotland were leading by a point when Jon Welsh was ruled deliberately offside in the 78th minute for playing the ball after a knock-on by a team-mate.
Joubert awarded the penalty, which outside-half Bernard Foley kicked to win the game, but World Rugby said the Wallabies should have been awarded a scrum instead because their scrum-half Nick Phipps had touched the ball.
"I genuinely feel for Craig Joubert," added Cheika, whose team will play Argentina in the semi-finals on Sunday. "It's so unfair.
"I have never seen that before. I am not sure why the decision had to be publicly reviewed and put out there.
"I really hope his fellow referees stand by him because, well, the fact I'm not allowed to say much about it says it all."
After the match, Scotland coach Vern Cotter said the television match official (TMO) "would have taken away any doubt".
But World Rugby said Joubert was not allowed to refer the decision as regulations only permit the use of the TMO on foul play or to determine the legitimacy of tries and kicks.
Joubert, who refereed the 2011 World Cup final, ran off the pitch after the final whistle without shaking hands with the players.
Former Scotland captain Gavin Hastings described his swift exit as "the worst thing I have seen on a rugby field in a very long time".
Ex-Scotland scrum-half Andy Nicol said Joubert was a "coward" while former England scrum-half Matt Dawson tweeted: "Craig Joubert you are a disgrace and should never referee again!"
Cheika was critical of the pundits' reactions, saying: "Unfortunately, in this instance, people have taken the game off the field and got quite personal about it.
"I can't make it sound like I'm looking after Joubert here because it's not like I've come from a background of pristine relationships with officialdom.
"But one thing I will say is that once the game is done and dusted, I'm as good as gold with anyone."
Kaplan, a veteran of four World Cups who holds the record for most international matches as a referee, questioned the overall standard of officiating.
"I'm just wondering whether this is a good look for World Rugby to be criticising their own assets," the South African told BBC Radio 5 live.
"Craig is definitely in the top four referees in the world and that's why he has been chosen to do the quarter-finals onwards.
"I'm not sure the standard has been high all the way through. I think there's been some holes in the make-up of the group.
"I think possibly there's four or five that are of the right quality, and the other six, seven or eight that are trying to get there."