United suffered their worst defeat at the Etihad Stadium since 2004, with goals from Yaya Toure and Samir Nasri adding to a Sergio Aguero brace either side of half-time.
Not even a Wayne Rooney consolation, which allowed him to become the top scorer in Manchester derby matches, could put a positive gloss on an awful afternoon for the Red Devils, who face Liverpool in the Capital One Cup at Old Trafford on Wednesday.
Moyes told his players the performance was simply not good enough. But he expects a positive response.
"If ever there was a group of players I would expect [a reaction from after a defeat] it is the Manchester United players," said Moyes.
"They react and that is what they will do. Every manager has bad days and bad results. I am no different.
"I have been here [at the Etihad] with Everton many times and I don't think I suffered a defeat like this with Everton.
"I talked with the players the same as I would at any other club. They are good pros here and they know when they are bang at it and when they are not."
United fell behind early on, when Aguero was left unmarked to turn home Aleksandar Kolarov's cross.
But the main damage came in a six-minute spell either side of the interval when Toure nudged home Alvaro Negredo's knock-down before Aguero added another from a Negredo cross and Nasri belted home after Jesus Navas had picked him out at the far post.