Samuel Eto'o scored from close range either side of half time for the hosts, with both goals originating from corners that United had failed to deal with.
Moyes was especially unhappy with the goal right on the stroke of half time, which saw a number of players vacate their positions too early, leaving Gary Cahill unmarked to set up Eto'o for a simple finish.
"The game came down to two set pieces and we didn't defend them well today. That was probably the difference," PA quotes Moyes as saying.
"While we were 1-0 down, we still had a chance. We were still in it but we gave away a free kick that led to a corner kick and we were terrible at defending the corner kick.
"We headed it out, we got rid of it and we didn't defend it well enough in the second phase and we found ourselves 2-0 down at half time."