Not including their extra-time League Cup match against Sunderland, United have won just two of their eight matches since the turn of the year following Sunday's 2-2 draw with bottom club Fulham.
They are nine points adrift of fourth-placed Liverpool and travel to Arsenal on Wednesday hoping to get their push for a Champions League place back on track.
But despite failing to beat teams like Swansea, Stoke, Sunderland and Fulham since the start of the year, Moyes maintains he still has confidence in his players.
He said: "We just go into the next game and take the teams on and challenge them.
"We've got a good team and there will be very few teams desperate to play Manchester United.
"The players are hurting. I can see every day that they're hurting because the results aren't going the way they want.
"They're really good professionals in the way they go about their work and what I see in training makes me feel they'll get results."
Steve Sidwell gave the Cottagers the lead in the 19th minute at Old Trafford and United struggled to hurt the Premier League's bottom side despite dominating possession and camping around the visitors' area.
They finally made the breakthrough when Robin van Persie tapped in from Juan Mata's cross with 12 minutes left and Michael Carrick scored with a deflected shot just over a minute later.
But after David de Gea could only push Kieran Richardson's shot into the air, Darren Bent headed in Fulham's equaliser in the fourth minute of added time.
United have now failed to win seven of their 13 home matches in the Premier League this season.
Moyes defended his tactics but admitted that the Fulham result was the lowest point in the season.
"Today was as bad as it gets. We dominated the game. Being one down was bad enough. The amount of attempts, chances and play we had was unbelievable. How we didn't win I have no idea." he said.
Fulham manager Rene Meulensteen, who left his job as a coach at United last year, felt his old team's game-plan was simple to read.
"I don't think there was any lack of belief as such. When I saw Manchester United I thought the game-plan was quite straight forward - get it wide, get it in.
"Whether it was from the full-back pushing on or the supporting wide man and midfielder, they put crosses in from wide angles from outside the box. We defended it well."
Meulensteen is hopeful that his side, who had lost 13 of their previous 16 league games, have reached a turning point after their battling draw at Old Trafford.
"I certainly hope and certainly felt if you came in the dressing room after that it felt like a win. Credit to our lads they hung in there."