Moyes' disappointing start to his United reign continued on Sunday when rivals Liverpool coasted to a 3-0 victory at Old Trafford victory.
The latest setback was another rude awakening for the Premier League champions, who could have lost by a greater margin as Brendan Rodgers' side showcased their title credentials with another impressive display.
United are seventh in the table and look certain to miss out on a place in the UEFA Champions League, as they are 12 points behind Manchester City - who occupy fourth place - and their city rivals have two games in hand.
Moyes' side also face a battle to reach the quarter-finals of the Champions League given they trail Olympiacos 2-0 ahead of Wednesday's second leg at Old Trafford.
The task of succeeding Alex Ferguson was never going to be easy, but Moyes revealed after Sunday's defeat that the challenge is proving tougher than he had expected following his move from Everton.
"The job was always going to be hard." he said. "Is it harder than I thought it would be? Yeah, I would say so."
"The players are capable of turning it round. We're not playing as well as we should be, we have to play better. we're going to have to make ourselves harder to beat.
"We''re also going to have make sure we're creating more and taking more opportunities - we've got a lot to do to do both those things.
"We're all desperate to put things right and play better and give the supporters something to shout about - we haven't given them anything on the field (on Sunday)."
Steven Gerrard scored two penalties and missed another before Luis Suarez added a third goal for Liverpool in a one-sided clash at Old Trafford.
Departing captain Nemanja Vidic was also sent off for the second time this year on another miserable day for the champions.
