With the score at 3-2 to Everton, Bernardo Silva was seen wrestling Merlin Rohl to the ground from a corner in the area. The referee waved play on and VAR declined to intervene, drawing immediate fury from Moyes.
Jeremy Doku equalised in the 97th minute to compound the injustice from Everton's perspective, a result that also handed Arsenal a five-point lead at the top of the Premier League table.
Moyes was blunt in his post-match assessment.
"I've seen it, I've had a look. If that doesn't get given as a penalty then it's an absolute free-for-all from now on. I might have to start coaching my defenders how to defend differently completely. It looks like now you're able to grapple and wrestle on the ground if you want. I'm absolutely amazed."
He linked the incident to a previous officiating grievance earlier in the week.
"This is on the back of a terrible decision at West Ham where we don't get a penalty there either. That's not the reason why we don't get the result tonight, but I think it's another pointer just to say that I find it really hard that that wasn't given. I think most football supporters will find that really difficult."
It was the third consecutive Premier League game in which Everton had dropped points in stoppage time — a statistic with no precedent in the competition's history — and a result that leaves them 10th, three points adrift of the European places.
Moyes was also asked whether Doku's equaliser coming in the 97th minute, when only six minutes of added time had been signalled, was a source of frustration.
"No, because we brought two subs on, but one of the frustrations about it is they're allowed to add 30 seconds on. So with six minutes over, if you add it up, we go to 97. But the difference was the third sub we made — our player was already off the pitch. So there would have been no need to add the 30 seconds, really. But because of the rule, I'm guessing he's just said: I've got to add 30 seconds on if you make a sub in injury time, which we did do."
It was Moyes's 17th meeting against Pep Guardiola as a manager without a victory. Manchester City face Brentford on Saturday before the final day at Manchester United, with the title now in Arsenal's hands.