Sylvan Ebanks-Blake slotted home the equaliser in the 75th minute with the visitors' first shot on target to cancel out Tim Cahill's early strike.
Moyes said: "In the first half we played well but when it's only one goal you always see it's a possibility. We controlled it in the first half but not the second.
"I thought we played fine in the first half and you probably thought the victory was only going to go one way but that's what the Premier League does to you.
"You've got to take your chances when you get them. We had some great chances to make it 2-0 in the second half. Tim Cahill played well but I don't know we gave their keeper enough to do."