Moyes hopes to end a dreadful week on a high on Saturday when Aston Villa come to Old Trafford.
The Scot suffered yet another blow to his credibility on Tuesday when his United team lost 3-0 to neighbours Manchester City.
That defeat left United 12 points adrift of the top four with seven games remaining.
United are guaranteed to end the season with their lowest points total in Premier League history, but Moyes insists any manager would have had difficulty turning what he describes as an "ageing" squad into title contenders.
"If Sir Alex were here this year it would be difficult for him as well and I'm sure he'd agree," the United manager said.
"People are aware there's a squad that is ageing, so it would have been a tough season for whoever was in charge of United this year. It could have been the case no matter what."
Moyes is bracing himself for the first sign of revolt against his reign on Saturday afternoon.
A group of supporters have clubbed together £840 to pay for a plane to trail a banner above Old Trafford which reads 'Wrong One - Moyes Out' during United's lunch-time kick-off versus Aston Villa.
A statement from the fans on the Red Issue website said the decision was "borne out of acute frustration - frustration at the poor results, lack of fight on the pitch and the unavoidable signs the David Moyes isn't up to the highest standards required to manage Manchester United Football Club.
"A significant proportion of Manchester United fans have had enough and unequivocally want David Moyes sacked."
It emerged on Friday that a bookmaker has also hired a plane to fly over Old Trafford.
It is understood that the bookmaker's banner is also anti-Moyes.
The beleaguered Scot insists he retains the support of most United fans despite his poor record this season.
"Everywhere I go, I get great support from Manchester United supporters," Moyes said.
"I went to dinner last night for Darren Fletcher and (some fans) came up to me and said: 'keep going, we understand exactly the situation the club and the team is in'.
"They were really supportive and every time I've gone to Old Trafford, the crowd have been great.
"I'm seeing it different to what a lot of people are seeing.
"I'm witnessing great support."
Moyes, meanwhile, has leapt to the defence of Marouane Fellaini, who is at the centre of a Football Association (FA) investigation over an alleged spit towards Pablo Zabaleta.
The FA has requested footage from Sky after a clip emerged on YouTube in which the United midfielder appears to spit near Zabaleta's head while he is lying on the turf during the Manchester derby.
"I've spoke with Marouane and he says it isn't the case," Moyes said.
"We will work with the FA if that is what we have to do. Marouane is adamant that at no time did he do that. I don't think it is completely conclusive, from what I've seen."