Darren Bent's 94th-minute equaliser saw United lose further ground in their bid for a Champions League place, leaving them nine points behind fourth-placed Liverpool.
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"I don't know if we could have done an awful lot more," he told the press. "We could have defended a couple of times a bit better or taken a few more of the chances we made.
"But we completely dominated the game and should have won comfortably."
Despite believing that his United side should have earned all three points, Moyes was scathing in his assessment of the defending in the build up to Bent's equaliser. A long punt up the field led to Steve Sidwell providing for Kieron Richardson, whose saved shot was diverted goal-wards by the England striker.
"We gave away a diabolical second goal," said Moyes. "If we had one failing it was that we should have gone to win 3-1. We had the chances.
"It was a game we should have easily seen out. We had no reason not to see it out.
"Was it lack of concentration? Yes, maybe. You could say there was a mental softness in that we didn't see the job out and get the job done."
Moyes shrugged off accusations that United became one-dimensional in their play on the day with the number of crosses in particular coming under scrutiny.
"If you're just going to look at the stats and pick the amount of crosses you need to look at the amount of passes too," said Moyes.
"I don't think we just went out just to cross the ball. I think a lot of people would say one of the one big things about Manchester United is that they do play with width and they do cross the ball. It's in the genes here."
Moyes admitted that he thought his side "could have taken a bit more care with some of our crosses and deliveries" and refused to concede that their bid to finish fourth was over.
When asked if Liverpool were too far away to catch, he simply offered: "We'll do our best."