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.
"We didn't play well enough to win the game," said Moyes.
"If you lose four you are not expecting to win too many.
"We conceded poor goals. We needed to get closer in the second half but they get away and score more goals.
"We never got a grip of the game and could never really stop them.
"We hoped to stem that tide in the second half. We got better as the game went on but it was too late.
"Manchester City played well and deserved the victory."
The one person Moyes exempted from criticism was Rooney, who now has 11 derby goals and four in three games following his return from a gashed head.
"Wayne Rooney was outstanding," said Moyes.
"He didn't deserve to be on the losing side today. He was first class."
United's second defeat of the campaign leaves them eighth in the table, five points behind joint-leaders Arsenal and Tottenham and rated as 9-2 shots to retain the championship.
"The start to the season could be a lot better," said Moyes.
"We did say it could be a difficult start.
"I wasn't convinced when the balls came out of the Premier League bag and I'm still not convinced."