With 11 matches of Moyes' debut season remaining United are seventh in the Barclays Premier League, 12 points adrift of the Champions League qualification places.
Under Sir Alex Ferguson, United won the title last year with four games to spare, but this term they are 18 points behind leaders Chelsea after suffering eight losses.
In his quarterly address to United fans in the club's season ticket holders magazine, Moyes confessed his team have not been up to scratch.
The letter, entitled 'A word from the boss' read: "While I knew that this job would be a challenge when I took it on, the difficult season we have experienced was not something that I envisaged, which I am sure is the case as well for you supporters - and my players, staff and I are desperate to compensate for that.
"You are accustomed to seeing a successful Manchester United and the backing you have given the players and I throughout the season has been incredible...the loyalty you have shown us has been magnificent."
Ferguson won the Premier League 13 times during his 26-year stewardship at Old Trafford, as well as a host of other European and domestic honours including two Champions Leagues.
Ferguson chose Moyes to succeed him despite the 50-year-old's lack of experience in managing an elite European club.
The former Everton manager is convinced he can turn things round at Old Trafford though.
"Over the years you have seen great winning sides here and, in time, I have absolutely no doubt that we will see great winning sides here again," Moyes added.
"We will do everything in our power to get the positive performances and results to do that, so that we can give you season ticket holders and all our supporters something to shout about..."
Moyes added: "In the long run, we will all come out at the other end, stronger for the experiences
Everything we have been through will make us a better, stronger team and club in the future."
Source : PA
Source: PA