The result was United's seventh defeat of the season already, leaving them 14 points behind league leaders Arsenal with just 16 matches left to play.
However, Moyes insists that he will "keep trying" to finish first and will not give up on the club retaining the title until it is mathematically impossible.
"We won't throw the towel in until we can't get there. The job is to try and finish first. I will keep trying to do that," PA quotes Moyes as saying.
"Before today we'd lost one in six in the league, and I didn't think there was a big difference between the teams today, not at all. The difference was our defending to set pieces. Nothing else."
United will face Sunderland in the League Cup semi-final second leg on Wednesday.