United have only picked up one win against the six sides above them in the Premier League this season, their sole success coming in a 1-0 triumph over Arsenal in November, and Moyes knows that record is a big factor in the club struggling to challenge the top four.
Recent victories over Olympiacos and West Ham have given United a much-needed lift, with the first of those wins securing qualification for the last eight of the UEFA Champions League.
However, Moyes acknowledges there is still plenty of room for improvement as his side aim to prevent Manchester City from claiming a third consecutive derby win when the two sides meet at Old Trafford.
"We're not as far away as many people would have us and I've no doubt it'll improve," said the manager. "We want to show we're still in there fighting.
"We want to perform better in the bigger games than we have done, I have no doubt about that. It'll be important to show the level of what we've got and I think we have got the level.
"We'll do everything we possibly can. We go out to win every game – not just the derby. It's no different. Obviously it means a lot more to the supporters and the city to win a derby game, but we go into every game with the same intention to win.
"In the last couple of games, a lot of the players have stepped up to the plate and performed. But I'm not surprised by that at all – that's what they're capable of and I've been saying that all year.
"We have a good squad with good players – we maybe haven't played as well as we should have, but I think we have those capabilities within the squad."
