Moyes' dismal debut season sank to a new low on Sunday when Liverpool eased to a 3-0 win at Old Trafford.
There was nothing fortuitous about Liverpool's first win at United's famous home stadium in five years.
In fact, United were lucky to get away without being given a really good hiding.
Other than a 1-0 win against Arsenal, United have not won a game against any of the top nine sides in the Barclays Premier League.
Moyes knew he would have a tough task on his hands emulating the achievements of Sir Alex Ferguson, but he never thought it would be this difficult.
"The job was always going to be hard," the United manager said.
"Harder? Yes I would say so yes."
The United fans have stuck by Moyes and there were no audible boos at the final whistle on Sunday.
Moyes knows performances and results will have to improve for that to continue though.
"Results will always dictate that but I can only tell you what I've seen today and the supporters were terrific," the Scot said.
United were an incredible 29 points ahead of Liverpool this time last year, but now they trail their old foes by 14 points.
The Merseysiders are almost certainly out of United's reach now and Moyes' focus is now set on an another improbable task - qualifying for the Champions League.
United are 12 points adrift of the top four having played two more games than their neighbours.
The United manager has not given up hope of finishing in the top four, however.
"It will be very difficult but it's not over yet so we have to keep working as hard as we can towards trying to do it," the former Everton manager said.
"I've been saying for a while we've given ourselves a long task and a long road to try to get back in it."
United's next difficult task is to try to overcome a two-goal deficit in Wednesday's Champions League match with Olympiacos at Old Trafford.
Moyes added: "The players are capable of turning it around. It's something to go for, it's another game and we'll do everything possible to make that work."
Meanwhile, United striker Wayne Rooney described Sunday's defeat to Liverpool - in which Steven Gerrard scored two penalties and Luis Suarez was also on target - as one of the darkest days of his career.
"It's one of the worst days I've ever had in football," Rooney told MUTV.
"It's hard to take. You have to give Liverpool credit - they played well - but it's difficult to take. Nobody wants to lose, especially in this way, in your own stadium. It's not nice."