Having won the Premier League by 11 points last season, the Red Devils now find themselves 11 points off fourth place after playing out a goalless draw against Arsenal on Wednesday evening.
The result saw both sides accused in some quarters of a lack of ambition to win the match, but Moyes is adamant his players retain their competitive edge.
"I see them [his players], I think they're great lads," he told reporters. "Their attitude to training, their commitment is first class. You saw it [against Arsenal] how good Vida [Nemanja Vidic] was, how good Rio [Ferdinand] was when he came on, they're a great group of players, very experienced players and they've been winners.
"They've all got medals and when you've won you want to win more. When you've won you want to win more so I think they're all still hungry and determined to be successful."
Victories for Liverpool and Tottenham on Wednesday further dented United's hopes of qualifying for the Champions League next season, but Moyes remains optimistic.
"I keep saying it, but I'll try to win the next game and see if we can pick it up," he added. "If there's one club in history that's been great at winning games in the second half of the season, putting pressure on other clubs, it's been Manchester United.
"We'll continue to try to do that and see if we can make it work."