Moyes refutes Pellegrini claim
United and City clash at Old Trafford on Tuesday and both teams have very different things to play for. A win for City would put them within three points of Barclays Premier League leaders Chelsea, over whom they have three matches in hand.
For United, the 167th Manchester derby is all about pride.
The Red Devils are 12 points behind their 'noisy neighbours' and their chances of making the top four this year are extremely thin thanks to what has been a dismal debut season for Moyes.
Last month Pellegrini appeared to poke fun at United's predicament.
The City boss said: "If you consider this season, there is just one club in Manchester and it is ours.
"But you cannot forget what United has done in previous years."
If the second sentence of that quote was supposed to be taken as a compliment, then it certainly has not gone down that way at United.
By using the words "previous years", the impression was that United's years of success were a thing of the past and that is certainly not something Moyes agrees with.
"Well Manchester United had lots and lots of seasons of domination," the United boss said.
"I don't think if I was a manager I would have turned round and necessarily said that we were the only club in Manchester because football does change, it goes in cycles."
The root of Moyes' misery this season has been United's form against their rivals.
Other than a 1-0 win over Arsenal, United have failed to beat any of their matches against the top nine sides in the league.
High-profile defeats to City last September, Chelsea at Stamford Bridge and the recent 3-0 humbling against Liverpool have left a mark on the United manager.
"They have definitely hurt," Moyes said. "They have hurt more because I joined Manchester United with big expectations myself - that I was coming to the winning football club.
"I've got a winning mentality and that's what I wanted to do, so I'm disappointed with myself and I'm disappointed that we've been unable to do that. But it has not been for the want of trying, that's for sure.
"We want to try and perform better in the bigger games than what we have done."
Moyes goes into the derby with an unwanted disciplinary issue on his mind.
The Scot has disciplined Chris Smalling after he was pictured apparently out in Manchester in the early hours of Saturday morning.
The Manchester Evening News published pictures of Smalling which it claimed shows the defender apparently singing in the streets at 3:15am.
Smalling had stayed in the north-west while the rest of his team-mates travelled to London for their Saturday evening clash against West Ham because of a hamstring injury.
Moyes is not happy with the 24-year-old's conduct, although he refused to reveal the punishment he had handed out to the player.
"I've dealt with it and I've spoken to Chris," the United boss said in a press conference.
"That would be as much as I would want to say on it."