Moyes' future again came under scrutiny after his side suffered their 11th defeat of the campaign against Everton on Sunday.
The 2-0 win gave the Merseysiders their first 'double' over United since 1970 but, despite the air of despondency around the club and its fans, Moyes is convinced they can take maximum points in the run-in.
Even with four victories - against Norwich, Sunderland, Hull City and Southampton - United will finish with their lowest points haul in a Premier League season and without a UEFA Champions League campaign to look forward to for the first time in two decades.
"We need to end the season on a high," Moyes told MUTV. "We want to finish by winning all of our games. We'll do everything we possibly can to make that happen."
Moyes' enthusiasm for the final matches is not shared by United central defender Rio Ferdinand who took to social media on Monday morning to vent his frustration at the outgoing champions' miserable campaign.
Ferdinand, who was not part of Moyes' squad on Sunday, said on Twitter: "Frustration and disappointment sums up the season so far."
And his feelings were shared by record signing signing Juan Mata who said: "I feel very disappointed today.
"This is how you feel when you spend two weeks waiting for a game, getting ready for it, and then things don't go the way you wanted.
"It happened in Goodison Park and the truth is this is not the first time, as you know. I hate this feeling.
"What the Premiership table shows now is something that neither the club nor the fans deserve.
"I hope the next game comes as soon as possible because, as you can imagine, this bad taste makes me mad."