Three Premier League defeats in their opening nine fixtures have left United in unfamiliar territory down in eighth place in the table, eight points behind leaders Arsenal.
However, with central defenders Rio Ferdinand and Nemanja Vidic both coming through this week's emphatic League Cup win over Norwich City unscathed after injuries, Moyes was upbeat in his news conference.
"We've started to string together one or two half-decent results and hopefully that will build a bit of momentum," Moyes said.
"We've been a bit up and down, winning one then losing one, so we'll hopefully try and get into a bit more consistency."
United scrambled to a 3-2 home victory over Stoke City last weekend, having twice trailed, and will be anxious to pick up three points at Fulham before facing leaders Arsenal at home in their next league fixture.
"It's a gap (at the top) and we have to work to try and close it. We'll take one game at a time and get closer to the top. That's the plan but there's a long way to go," Moyes said.
Robin van Persie was rested against Norwich because of some niggles but is expected to return to face Martin Jol's Fulham at Craven Cottage, although Danny Welbeck is ruled out with fluid on the knee.
The return of Ferdinand and Vidic, who have not started a league game together since the 4-1 defeat at Manchester City in September, has given Moyes plenty of defensive options.
"I think both (Vidic and Ferdinand) are very close to full fitness," Moyes said. "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.
"Van Persie has been fine. He's trained well and worked quite well this week so hopefully he will be okay."
Like Moyes, Fulham manager Jol has been under scrutiny with his side just two points above the bottom three and knocked out of the League Cup by Championship (second division) Leicester City.
Fulham have won only once at home in the league this season and the attacking partnership of former United player Dimitar Berbatov and Darren Bent is yet to click.
"Tomorrow is a big game for us and if we can get a good result then the world will look different," Jol said.