After losing to Everton on Wednesday, Moyes' side were unable to find a way past Newcastle United, although the visitors had a slice of luck when Vurnon Anita's handball on the goal line was not noticed by referee Andre Marriner.
Yohan Cabaye's 61st-minute strike sealed a 1-0 win for Alan Pardew's side, and sent Moyes' men to their fifth defeat of the season – the most games they have lost at this stage of the season in 12 years.
United dropped to ninth in the Premier League table after the defeat - 12 points behind leaders Arsenal, who face Everton on Sunday.
However, Moyes remains defiant and believes his side can turn their fortunes around and still compete for the title.
"(I'm confident because of) the players and because I'm working with the champions," he said. "(They are) the same players that won the Premier League.
"We're needing something to go for us to give us a bit of confidence. We could have done with a goal just to get us in front and I thought the goal was really unfortunate.
"His (Anita's) hand definitely stops the ball going in the net so you can decide whether that's a penalty or not.
"If we'd come out on top in both games (against Everton and Newcastle) I don't think anyone could have said much about it but we've not and because we're Manchester United we have to do better.
"We have to play better, pass it better, make more chances and take our opportunities when they come."
