Cahill was forced to come off in the second half on Saturday after Kompany caught the Socceroos star with a stamp on his shin.
Kompany had jumped to avoid a rash challenge from Cahill and landed on the midfielder's leg as he came down.
Cahill was booked for the tackle before being taken off, but Moyes believes it was Kompany who deserved punishment.
He was relieved that Cahill has only suffered bruising to his shin but felt the damage could have been far worse.
"The boy (Kompany) does him," Moyes told the BBC. "He definitely sees his shin going in and stands on it. People who have been players know what I am talking about.
"I don't think it is too bad. It just looks like bruising. But they are the ones where it doesn't take much to crack your shin.
"The officials seemed to spot most other things. But they did not spot the big one. Referees are judged on big decisions."
Moyes was not impressed by the performance of World Cup final referee Howard Webb and his officiating team, whom he felt got a key decision wrong in the build-up to Mario Balotelli's opener.
"Overall, we found the way the officials treated us really difficult to take," Moyes said.
"We found it difficult to talk to them and found the fourth official was very much the same. What we want is a bit of consistency."
Source: AFP
Source: AFP