Joleon Lescott grabbed Everton's winner and Moyes said: "We missed the flair of Steven Pienaar and the strength of (Ayegbeni) Yakubu. But we know this will be a difficult month.
"But we defended really well, and Tony Hibbert did a really good job on (Martin) Petrov, who has been terrorising defenders.
"It is getting really tight now for fourth spot. Looking at the way the results are going, we know we just have to hang in there and hope we are in the right place at the end of the season. But that will be tough, there is nothing between anyone these days in the top half."