Moyes was frustrated his side were unable to break Swansea's resilience.
The result meant they missed the chance to gain ground on Tottenham in the battle for a top-four spot while Chelsea pulled further away.
Moyes said: "We are a bit frustrated but Swansea did a really good job in midweek on Chelsea, not dissimilar (to this). We needed to play a bit better, pass it a bit quicker and be a little bit cleverer in the final third.
"We had three or four good opportunities, but just not perfect (ones). I couldn't turn around and say I thought anyone missed a real sitter. I thought we kept going, we tried to do the right things.
"We could have done it better but I can't fault the players for their effort. We just couldn't get the ball over the line today, that was the thing.
"Apart from one Michu opportunity in the first half when he chipped it and Tim flicked it on to the bar, I don't think we were threatened that much.
"They have had a busy week, a hard week, and it is a great point for them. We are just disappointed we couldn't turn our opportunities into goals."