City are big favourites for the derby at Old Trafford due to their higher league standing and the fact that United have struggled against the top teams in the league this year.
A 1-0 victory against Arsenal aside, Moyes' men have not beaten any of the sides in the top nine in what has been a truly disappointing maiden season for the Scot.
Moyes wants that to change on Tuesday though.
"We we want to try and perform better in the bigger games than what we have done," the United manager said.
"It will be important for us to show the level of what we have got.
"I think we have got the level and we are not as far away as many people would have us and I have no doubt it will improve. We want to show we are still in there fighting.
"We will do everything we can to win. We go out to win every game, not just the derby game.
"Obviously it means a lot more to the supporters and the city if you win a derby game."
United are 12 points behind City, and Manuel Pellegrini's men have played two less matches.
The Red Devils go into the match on the back of encouraging wins against Olympiacos and West Ham though.
United had to field Michael Carrick at centre-half at Upton Park because of injuries to Chris Smalling, Jonny Evans and Rio Ferdinand. Nemanja Vidic was also absent through suspension.
The United captain remains banned for the visit of City, but Moyes would not give away anything about the fitness of the three injured players.
"For this Barclays Premier League game we'll do everything we possibly can to get the [injured] players back," was all that Moyes would say when questioned on the matter at his pre-match press conference.
Should none of the trio be fit, Moyes is certain he has a good enough back up in Carrick.
Carrick performed well keeping Andy Carroll quiet on Saturday, but the pace of Alvaro Negredo, who is expected to lead the line for City in the absence of the injured Sergio Aguero, will present the England midfielder with a different and perhaps more dangerous threat.
Moyes said: "Michael did great at centre-half. He's played there before so it wasn't a problem.
"We even considered putting (Marouane) Fellaini back there as well, so I think we've got people who can do that if we have to.
"We gave Patrice Evra a rest but if we have to, I think we can put him there as well and he would cope manfully.
"It was great that the squad mucked in and that's the way it should be, when you are short in areas and it's all hands to the pumps.
"We were short on Saturday and Michael certainly played really well."
Rooney made Saturday's game in east London one to remember as he scored a stunning goal from just inside the West Ham half.
The England striker then added a second to move above Jack Rowley into third in the club's all-time top scorers list.
Moyes thinks Rooney may have a big bearing on the outcome of the derby, which comes six months after City hammered United 4-1 at the Etihad Stadium.
"Wayne's form throughout the season has been very good and his goal capped off what everybody is aware he's capable of," the United boss said.
"He's spoken about a lot because of his ability as a footballer. He showed it on Saturday in a way maybe everybody is aware he's capable of, but which many others maybe aren't capable of.
"But more importantly for me is how well he's played for the team - that's a big thing.
"From the first game he's been a great team player. I don't know if he'll be the key man because this game has got many, many top-class players in it, so I wouldn't necessarily say he's the main man, but he's certainly one of them."