The Toffees were forced to share the points for the 10th time this campaign tonight as Southampton held them to a stalemate at St Mary's.
"We are a good bit through the season, we have had a lot of draws and we need to look to win it," Moyes said.
"We tried in the second half today and we will certainly try to ensure we win more than we draw in the second half of the season.
"I was frustrated with how we played and frustrated in the second half that we did not get the goal. We got better in the second half. In the end they had the better of the first half and we probably had the better of the second."
The result leaves Everton three points behind Tottenham Hotspur in the chase for Champions League qualification.