The Hammers dominated possession throughout the match, but needed a last-minute equaliser from Andy Carroll to salvage a point.
Moyes, however, believes that his side created enough chances to deserve more than a draw.
"I thought we played really well. We played good in parts of the game, it was just the fact we went one behind, because if anyone was going to score first I thought it would be us," Sky Sports News quotes the Scot as saying.
"We got the ball forward well out of the back, we just didn't have something different up front. But we did on the bench, I thought all the subs who came on made a big difference, we've not had that very often and I'm very pleased to get them back.
"We didn't need to make subs, we were playing well and in their half, I thought the goal would come and I thought we could score late on. The minute we went a goal down, we had to find a way of doing things differently.
"I've seen a couple of the goals that were ruled out and it looks like the right call. We're in a good position, a lot better than when I came in."
West Ham are 14th in the league table following the draw, seven points above the dropzone.