The Red Devils bounced back from their 4-1 mauling at the Etihad Stadium in the perfect manner, with Javier Hernandez grabbing the only goal in a Capital One Cup third round victory over another of their fierce rivals.
And Moyes could not have been more delighted with the response.
"It was important the whole club showed we were hurt by Sunday," said the United boss.
"We didn't perform to our levels.
"Now the players have gone out to get us a big result. I am really pleased with them."
Moyes' sceptics had a field day following Sunday's hammering at Manchester City, which led to claims the Scot is incapable of securing victories in the biggest matches.
For the moment, they have been silenced, as Luis Suarez's return from a 10-match suspension ended in disappointment.
And, after being told he had now made the best start of any new United manager since Matt Busby in 1946, Moyes claimed he will eventually do it for good.
"Everybody seems to be picking a stat out - I have not won here or I have not done that," said Moyes.
"That is one of the good stats.
"I have not had that many good ones. But that is one of the better ones.
"It is not frustrating.
"I will sort it. I will fix it.
"I will turn it round.
"I have no doubt about that."
Moyes did confirm England midfielder Tom Cleverley was ruled out with an injury which watching Three Lions boss Roy Hodgson must hope is not too serious.
But, after making eight changes - and naming Wayne Rooney captain - the United boss saw his team perform with more attacking conviction than they have done in most of their more important matches this season.
"It certainly was," said Moyes, when asked if his reaction at the final whistle was one of relief.
"It was a big game for us. We had lost at Anfield a few weeks ago and at the Etihad on Sunday and we wanted to put that right.
"Every game, everybody is either a first for something or it is a monkey off my back.
"It is going to be the way isn't it?"