A second consecutive home defeat for the Reds also meant an FA Cup exit at the first hurdle, and the boss said his team couldn't convert possession into clear-cut chances.
"We didn't do enough to win it; we made some opportunities but they weren't enough," Moyes told BT Sport. "When we went down to 10 men we just needed to see it out and try to force a replay, but we didn't get that far. We kept trying to go for it and got caught a little bit and lost the second goal."
That said, the United boss was pleased with his side's general play, having enjoyed the bigger share of possession in the opening 45 minutes, but Moyes felt the Reds could have made more of that dominance.
"I think we played quite well in the first half," he said. "We got near the edge of the box quite regularly, but we didn't quite make the opportunities to score more goals."
Adding on MUTV, Moyes said: "I thought [Wayne Routledge's goal] was the only time they had been up the park in the first 15 minutes. For us to lose a goal was poor, but we got back right away. We had time to make more chances, make more goals. We maybe abused it, the amount of opportunities we got, and didn't finish one better.
"That's the disappointing thing as we'd come back from a goal behind and I thought for long periods we had control of the game, but we didn't get a goal or create enough chances."