Moyes watched on as Steven Gerrard scored twice from the penalty spot before Nemanja Vidic was shown a second yellow card for a foul on Daniel Sturridge inside the penalty area.
Gerrard missed the ensuing spot kick before Luis Suarez made it three and ensured Liverpool of their first win at Old Trafford in seven attempts.
United were subdued throughout as they slipped to a sixth home defeat in all competitions this season.
And after suffering a further blow in his debut season with the champions, Moyes was surprised by his side's below-par showing.
"It wasn't what we expected, I felt as if the players looked in good shape and good fettle going into it but we just didn't get to the standards that were required to beat Liverpool," he said.
"I said all week, I've not seen that. I've seen confident players, well-motivated and hard-working (players).
"We didn't start the game as well as we'd like but I actually thought we grew into the game a bit better but the (second) penalty kick changed that.
"Liverpool played well and we didn't play as well as we can. We'll work to make that better."
The defeat leaves United 12 points off fourth place with just nine games to rescue their league campaign.
