Lallana's goal came in the 89th minute and Moyes said that he was "disappointed" in his team's inability to close the game out.
"We had a few chances to wrap it up and [I'm] disappointed," Moyes told Sky Sports News.
"We had a few chances to wrap it up and when you lose a goal like we did from a corner it's disappointing. We had pockets of good play during the game, but we could not finish it off.
"I'm looking to build on things every week and find that [consistency], and all we can do is try to win the next game."
The draw leaves Moyes's side eighth in the Premier League.