The new Red Devils manager's only notable summer recruit was the £27m signing of Marouane Fellaini, who has only started four Premier League games in a difficult beginning to the season for the champions.
United currently sit in ninth place, 13 points behind leaders Arsenal, and Moyes has admitted that the playing ranks at Old Trafford need reinforcing, and will be in the "coming months and transfer windows".
"We are making sure everyone has an opportunity to show the new manager exactly what they can do," he told reporters.
"We are trying to be as fair as we can to the players who are here. We have really good players. These are near enough all the players who were involved last year. Hopefully we can get them in top form.
"I have a good squad. Can I improve it? Of course I can. Am I going to improve it? Yes I am. Undoubtedly we will alter things in the coming months and transfer windows. Will they come in January? I don't know."
United travel to Aston Villa on Sunday and will be leapfrogged in the table by their opponents with defeat.