The incident occurred in the second half, when the game was still goalless. Cahill was booked for a rash challenge but as Kompany took evasive action, he landed on the midfielder's leg. It quickly became apparent Cahill would not be able to continue and he was replaced by Louis Saha.
"The boy 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."
In fact, Moyes was not impressed by the performance of World Cup final referee Howard Webb and his officiating team, whom he felt showed inconsistency in the way they handled the game and 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. We found it difficult to talk to them and found the fourth official was very much the same," said Moyes.
Everton finished the game with five yellow cards compared to City's one, which Moyes did not feel was a fair reflection of how the game panned out, pointing out one contrast where an Everton player did not get a free-kick for a challenge very similar to one Leon Osman was booked for earlier in the game.
"There is a challenge on the edge of the box by Vincent Kompany on Louis Saha that was not much different to the one by Leon Osman on Micah Richards," he said.
"What we want is a bit of consistency."
Source: PA
Source: PA