The Toffees finished sixth after Moyes' 518th match in charge ended in a 2-1 defeat at Chelsea, with Steven Naisimith on the scoresheet for the visitors.
"In truth we've probably done as well as we can do at Everton," Moyes said.
"We've pushed close to try to break into the top four, up until about three weeks ago, it just started to get away from us.
"I'll go into Finch Farm [Everton's training ground] some of the days next week and make sure everything's in place for whoever the incoming manager is.
"Most of it is anyway, but I'll just make sure that everything's as ready as I can leave it."