Moyes' difficult first season as United manager reached a new low on Sunday when rivals Liverpool coasted to a 3-0 Premier League win at Old Trafford.
That defeat piled more pressure on the former Everton boss, with the defending champions seventh in the table and looking almost certain to miss out on a place in next season's UEFA Champions League.
United's fate in the competition this term rests on the second leg of their last 16 tie against Greek champions Olympiacos, who boast a two-goal advantage from the first meeting.
Reacting to more questions about his future, Moyes insisted that he is the right man for the job and said he still has the backing of owners the Glazer family.
The Scotsman said on Tuesday: "My future has not changed one bit.
"The biggest assurance is they (the Glazers) let me get on with the job, we're making big plans for a long-term future, that's why it's a six-year contract.
"This club is not one that works on a short-term vision, it works on a long-term vision."
Old Trafford was a fortress for much of Alex Ferguson's reign, but United have suffered six home defeats in all competitions in Moyes' maiden campaign at the club.
And the 50-year-old has urged his side to address that poor record, starting with Wednesday's crucial Champions League showdown.
"Results at Old Trafford have been disappointing but it's not for want of trying." he added.
"I've told the players we must start giving something back and performing."
