There were four yellow cards shown to Chelsea players inside the first 34 minutes but Moyes felt Rogers should have received a second of his own and been sent off before half time.
Rogers was booked for running at James Tarkowski to complain about the defenders robust off-the-ball barge on Moises Caicedo.
Then Rogers engaged in a fierce fifty-fifty challenge with Everton midfielder James Garner. Both players felt the other had committed a foul.
Paul Tierney brandished seven yellow cards during Everton vs Chelsea, but David Moyes feels he might have shown Morgan Rogers one more
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Morgan Rogers and James Garner both required treatment after a crunching fifty-fifty
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Rogers was already on a yellow card but VAR checked and cleared the tackle and deemed it a fair challenge not worthy of awarding a foul on either side.
But after the game, Moyes said he felt Rogers should have been punished more harshly and sent off.
Moyes said: “We’ve got referees who we want to be the best in Europe, who think they’re the best in Europe because they let things go.
“I’ve had a wee look at the Morgan Rogers tackle on Jimmy [Garner], which some may have said something different [about]. And I think that might have made it a second yellow. But that wasn’t the case.”
Rogers joined Chelsea from Aston Villa for £117million in the summer and has made a superb start to life with the Blues.
He has scored four goals in seven Premier League outings for Xabi Alonso’s side.