"We didn't play well today, Blackburn played better than us and we were a little bit fortunate to come away with a point," Moyes told Sky Sports News.
"We've not played well enough and we're going to have to try and improve.
"When you're in your home games you always want to win them. We have to see it as what was a chance for us to pick up all three points and we didn't do so."
The draw means that Everton remain in the bottom half of the Premier League table.