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.