Although United are eight points adrift of leaders Arsenal after 10 games, the gap to second-placed Chelsea is just three points after Saturday's fixtures.
Goals from Antonio Valencia, Robin van Persie and Wayne Rooney guided the reigning champions to a 3-1 win at Fulham and Moyes feels that there is more to come from his side.
"Our job is to climb the league table. We want to get nearer the top and I've no doubt that by the end of the league season we will," said the United manager.
"Where we are now I don't think is really that important, except that you don't want to let teams get too far away from you.
"We've got to try and make sure they don't and we're going to have to keep building on recent performances."
Fulham were left stunned as United roared into a three-goal first-half lead during what Moyes described as "a blistering period in the game".
The Scot expressed particular satisfaction at the performances of Van Persie and Rooney, who now boast a combined tally of 16 goals in all competitions this term.
Moyes added: "They both made the goals for each other; (there was) good link-up play, so I just started to see really good signs from the two of them and it was great that they both got on the scoresheet because that's what forwards do.
"I've always said you need these boys to get a hat-load of goals if you're going to be successful.
"They are both incredibly talented and they understand each other and the talents the other has got. They are both excellent players."
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