In 12 Premier League fixtures since Moyes succeeded Sir Alex Ferguson, United’s sole victory against sides around them came against Arsenal in November.
Manuel Pellegrini’s City target their third consecutive win at Old Trafford to close the gap on league leaders Chelsea, but Moyes hopes denting the title aspirations of their “noisy neighbours” can be a shot in the arm for his own team.
“We want to try and perform better in the bigger games than what we have done,” said Moyes.
“It will be important for us to show the level of what we have got. We are not as far away as many people would have us and I have no doubt it will improve.”
United are without injured striker Robin van Persie, while central defenders Jonny Evans and Chris Smalling could also miss out with injury and Nemanja Vidic is banned.
Midfielder Michael Carrick deputised in central defence in last Saturday’s 2-0 win at West Ham and Moyes would have no hesitation in deploying the England international in the same role again.
“We were short on Saturday and Michael certainly played well. He’s played there before so it wasn’t a problem,” he added.
“It was great 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 pump.”
City can leapfrog Liverpool into second place and close the gap on Chelsea to three points, and with two games in hand, if they can record a fourth straight league win.
They welcome back captain Vincent Kompany after suspension, yet Pellegrini is adamant City are not favourites to triumph.
“Just because Manchester United have had a difficult season it does not mean we are going to win,” said the Chilean.
“We are in a good moment, but we are playing against a big team in their own stadium, so I don’t think we are the favourites.
“The derby has special importance for the fans because they enjoy winning against Manchester United, but for me all the games are special because you have to get three points.
“We are just trying to fight for the title. We must go game by game.”