David Moyes believes that, if Manchester United show the same level of creativity and desire at home to Manchester City on Tuesday as they have done in their past two matches, they can triumph against their local rivals and secure what would arguably be the club's most important win of a difficult season.

United head into the derby four places and 12 points behind Manuel Pellegrini's side but with good confidence following their Champions League victory over Olympiakos last Wednesday – which secured their place in the last eight of the competition – and Saturday's 2-0 win at West Ham United, when United put in probably their best domestic display under Moyes. The manager has got the reaction he was looking for after the humbling defeat by Liverpool at Old Trafford eight days ago, after which it appeared his future at the club was under threat for the first time since his arrival in the summer, and he has now called on his players to build on their encouraging form.

"We go in [to the derby] after a better showing and, if we play as well as we did at West Ham, then we'll make opportunities and, if we play with the same heartbeat we showed against Olympiakos, then we'll be very hard to play against and have a big spirit in the game," said Moyes. "Hopefully we're starting to pick up and play better. We're certainly going into our next game confident and ready to get a result."

United entertain City without their captain, Nemanja Vidic, who serves the final game of a two-match suspension, and top-scorer Robin van Persie, who may miss the rest of the campaign with a sprained knee sustained in the win against Olympiakos. But they face a side also missing one of their key men in Sergio Agüero, who has a hamstring injury, and buoyed by the weekend display at Upton Park, when the visitors played with a level of control, invention and purpose rarely if ever seen this season.

Moyes' two major signings as United manager, Marouane Fellaini and Juan Mata, delivered possibly their best performances since arriving at the club – although the former could yet face FA action for a late tackle on James Tomkins on Saturday which the referee Lee Mason did not see but Sam Allardyce, the West Ham manager, said deserved a red card – while Wayne Rooney excelled as United's captain and spearhead and scored both of his team's goals, the first of which was a stunning 57-yard strike of a bouncing ball.

"It's the sort of magic that makes you talk about a top player and Wayne is a top player," said Moyes. "I also thought the two of them [Mata and Fellaini] were excellent against West Ham.

"We know Juan can play two or three different positions and that was always going to be the case. His performance behind Wayne was excellent."

Michael Carrick also performed impressively against West Ham, particularly so as the midfielder was deployed at centre-half against his former club due to the absence of Vidic and, through injury, of Jonny Evans and Chris Smalling. Ahead of tomorrow's match, the 32-year-old has made it clear that the United players have learnt from their poor performance against Liverpool and go into another significant contest fully focused.

"We understand the fans and the result they want and for us players it's exactly the same – we feel the same," said Carrick. "I've been part of this club for a long time now and you know what means a lot. This [the derby] is certainly one of them. It's a one-off game against your local rivals and in a derby like that you always want to come out on top."

United have lost their last two games against City, the most recent a 4-1 drubbing at the Etihad Stadium last September. The champions' season has faltered on a consistent basis ever since and domestically at least there is little left for them to play for bar salvaging a Europa League place and stopping their nearest rivals winning a second Premier League title in three seasons. City head to Old Trafford in third, six points behind leaders Chelsea but with three games in hand.

"I don't think for us as players that's something we can really look at," added Carrick. "We just have to look after ourselves and do the best we can for us. There's going to be twists and turns in the title race; most of the teams involved still have to play each other. We just want to win this game for ourselves and keep the run going. We'll go into the City game looking forward to it.".