The home side created the majority of the chances but the closest they came was when Marouane Fellaini headed over in the first half and Tim Cahill hit a post in the second.
Everton have now not won in seven games, and Moyes said following the draw: "It certainly wasn't their attitude. I questioned it a bit in the last home game against West Brom (a 4-1 defeat) but they went for it today. They were industrious without having the quality required but we just missed chances."
He added: "I don't think you get better chances in the Premier League than we did today - three or four opportunities.
"The longer we didn't take them the more frustrated we got and the more anxiety came into our play and the crowd. We just have to take those chances. The crowd know we have been here before in a similar situation but I think the worrying thing is we are not beating teams at Goodison who, over the years, we have done.
"I am saying 'Is it something else other than just not scoring goals?' and I am finding it hard to look further than that.
"It wasn't just the centre-forward today, there were chances shared around the team and no-one converted any of them.
"The anxiety is coming from the form and our position (two points above the relegation zone).
"We are all wondering where we are going to score a goal.
"I tried to freshen things up with 20 minutes to go and I thought we were worse then than at any time in the game. I thought we looked more open and a poorer team and I thought my substitutions today were poor and I made the wrong choices."
Source: PA
Source: PA