Build-up to the game was dominated by a planned protest against Moyes' management of the struggling champions, with a plane trailing the message 'Wrong One - Moyes Out' flown above Old Trafford during the contest.
Despite that, the overwhelming majority of the crowd remained firmly behind the manager, jeering the overhead display and cheering the Scot's name throughout much of the fixture.
After a 3-0 defeat to Manchester City in midweek, Moyes expressed his belief that predecessor Alex Ferguson would have likely also strugled to maintain United's run of success and reaffirmed his commitment to Old Trafford long-term.
He said: "I just wanted everyone to know I'm the manager of the club and I want you to know where I am.
"I'll be standing at the side of the pitch every week and that's my job. I found the support inside old Trafford has been terrific.
"I think today, if ever there was a show of support for the football club and the team it was today, the support inside of Old Trafford it really was.
"The truth was I was focused on the game today, that was my be-all and end-all to make sure the team won the game, nothing else.
"I speak to people outside and I have the same feeling everywhere I go of the support for this football club and the majority inside the ground and I thought they got right behind the club and our team today."
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