Moyes said: "I didn't think we deserved to lose like that but in the end we did because we got caught by a counter attack and the set piece we conceded was terrible. People need to do their jobs better than they did today."
The Everton boss went on to admit that his team lacked the attacking creativity they have shown in recent games.
"They came off the play and allowed us the ball and we played some good stuff at times, but in the final third we didn't have the players in form or the cutting edge to make a difference," he added.
"We're really disappointed to lose, the way it ended up, I am looking for them to be stronger. The boys at the back, there is no need for them to concede a goal.
"But we did concede a goal and we had to go chasing and we left ourselves a bit open. Maybe when it was 0-0 I should have settled for a draw but I wanted a bit more than that."
The result sees Everton slip down one place to fourth in the Premier League table.