The Red Devils slipped to defeat at Stamford Bridge thanks to a Samuel Eto’o hat-trick, which leaves them 14 points adrift of leaders Arsenal.
With the season past its midway point, it appears that the defending champions have their work cut out to overhaul such a gap, particularly with the top three in such good form.
Jose Mourinho claimed after the game that United are now out of the battle, but Moyes says that his aim is still to secure the title:
“What we don’t do is throw the towel in until we can’t get there.” He is quoted by BBC Sport.
“The job is to try to finish first and we’ll try to do that.”
United are also some way off of the top four, and face a real fight to overhaul the likes of Liverpool, Tottenham and Everton for Champions League football.
Although he concedes that his side are not in an ideal position, Moyes says that his spell at Old Trafford is a long-term project:
“This is a project. I know what I’m going to do and there will be changes as we go along the journey.
“It is a massive challenge. I hoped we’d be in a better position than we are, but we are not.”