Moyes has had a mixed start to life at Old Trafford since succeeding Sir Alex Ferguson in the summer but there have been signs of recovery in recent weeks.
United have won their last three matches in all competitions and are unbeaten in six since a shock loss to West Brom at the end of September.
Moyes said: "We have started to pull together one or two half-decent results. Hopefully that starts to build a bit of momentum.
"We were a little bit up and down at the start of the season - winning one, losing one - so we are hoping to get more consistency and our form follows that.
"It has been good, the games we have won, but we have still got a bit to go. I don't think the dust is all settled down, not at all.
"We have still got more days where it might not go our way but I think the team is beginning to look a little bit better."
Moyes certainly feels he is now more attune with the players he inherited.
He said: "I am beginning to get to know them much better.
"I am beginning to see them and get an understanding of what they can do, what they are capable of.
"But in the same breath, we are still trying to find a side that gives us the consistency week in, week out and which we can say, 'Yes, this is the performance level we want to get'.
"In a lot of ways we are still striving to find that."
United head into this weekend's Barclays Premier League trip to Fulham eighth and trailing leaders Arsenal by eight points.
Moyes is not overly concerned by the gap - the champions face the Gunners next week - and believes his men can slowly pull their way back into the title race.
He said: "It is a gap we have to continue to work to get closer to.
"We try to take one game at a time, get a bit closer to the top end. That is the plan but there is a long way to go."
Moyes, speaking at a press conference to preview the Fulham game, avoided getting drawn into a war of words with Manchester City's Yaya Toure over their league challenge.
Toure has been quoted saying United are "really struggling" and will find it hard to retain their crown.
"I didn't see that so couldn't comment on it," Moyes said firmly.
One area of criticism Moyes did respond to was the suggestion he looked to strengthen the wrong areas in the summer.
United fared badly in the summer transfer window, missing out on a number of targets and eventually signing only Marouane Fellaini on deadline day.
Yet as the emergence of Adnan Januzaj has since proved, United remain well served in many areas.
Moyes said: "We have said before that Adnan can play any one position off the left, off the right, in behind (the striker), and he can play as a centre forward as well. He is a really good centre forward.
"Shinji (Kagawa) can do two or three jobs as well. That is why in the summer we didn't need people in those roles, which a lot of people suggested.
"We have a lot of players who can play there. I am pleased with what we have got.
"We have got variations and we will try to use them when we see fit."
Striker Javier Hernandez has given Moyes a selection headache after scoring a winner off the bench against Stoke last weekend and then grabbing two against Norwich in the Capital One Cup on Tuesday.
The manager said: "He is starting to do what he has done over the years - score goals. Long may that continue."
Moyes' opposite number this weekend, Martin Jol, has been under pressure after an indifferent start to the campaign and the Scot can understand his position.
Moyes said: "Fulham are a strong club, but it is still one of the clubs people might look at and think might be in the bottom half of the league, near the bottom end.
"So maybe it shouldn't be too big a surprise. Martin is a good manager and has done a good job wherever he has been."
United have not commented on media reports that Brooklyn Beckham, son of their former star and England captain David, has trained with the club.
Moyes said: "I wouldn't talk about any young players at the club.
"You don't ask me about any other young players that are here, so you wouldn't expect me to answer that would you?"