The Old Trafford outfit have endured an indifferent start to their title defence, winning four and losing three of their nine top-flight fixtures.
United have triumphed in their last three matches in all competitions and are undefeated in the previous six.
And Moyes has now targeted a run of victories to close the gap on the teams above them.
"It's a gap we have to try to work to get closer to," he said ahead of Saturday's visit to Fulham.
"We'll take one game at a time and try to start getting a bit closer to the top end. That's the plan but there's a long way to go.
"We've started to put together one or two half decent results and hopefully that starts to build up a bit of momentum.
"We've been a little bit up and down at the start of the season, winning one, losing one, so we're hoping to get a bit more consistency and then our form follows with that."
Moyes has also been handed a boost with the news Robin van Persie will be fit to start against Martin Jol's side, with centre-back pairing Rio Ferdinand and Nemanja Vidic also coming through the 4-0 League Cup victory over Norwich City unscathed.
"Van Persie has been fine. He's trained well and worked quite well this week so hopefully he will be okay," he added.
"I think both (Vidic and Ferdinand) are very close to full fitness. They showed that in midweek when playing Premier League opposition.
"They both played for 90 minutes so I can't see any reason why they wouldn't be ready to be selected or involved."
